Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@alaingoudemand9818
2 жыл бұрын
Ä
@QuentinStephens
2 жыл бұрын
In your first method you state that a = xy / (x+y). I think it would help if you derive that.
@bfelten1
2 жыл бұрын
I agree. Rather than spending all that time with trivial calculus...
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@wiwi355
2 жыл бұрын
From Thales theorem : FD/AB = CF/CA, or a/x=(y-a)/y Then you put all a to the left side. You should find a=xy/(x+y)
@Tmwyl
2 жыл бұрын
@@wiwi355 Aha.. That helps. Thanks
@montynorth3009
2 жыл бұрын
I used similar triangles, the only difference being that I used the large triangle ABC with triangle FDC. (12-a)/a = 12/20 (12-a)/a = 3/5 Cross multiplying. 5(12-a) = 3a 60-5a = 3a 60 = 8a 7.5 =a
@wtspman
2 жыл бұрын
I did it that way, too.
@PreMath
2 жыл бұрын
Excellent! Thank you for sharing! Cheers! You are awesome 😀 Keep it up 👍
@godwinstaples5270
2 жыл бұрын
This is how I did it.
@PMSTACKER3000
2 жыл бұрын
likewise
@markasiala6355
Жыл бұрын
I like this method as well. It appeals to similar triangles directly that more people have had exposure to than jumping in on a lesser known result that is derived from similar triangles.
@s1ng23m4n
2 жыл бұрын
Without using similarity: Draw a diagonal of a square to the hypotenuse of the big triangle. Area of big triangle = 12 * 20 / 2 = 120. Area of big triangle = the sum of two triangles formed by drawing a diagonal. One triangle has area 1/2 * base * height = 1/2 * 20 * x = 10x. Second triangle has area 1/2 * 12 * x = 6x. So area of big triangle = 16x and 120 as we calculated earlier. 16x = 120 => x = 120/16 = 60/8 = 30/4 = 15/2. A = x^2 = (15/2)^2
@PreMath
2 жыл бұрын
Excellent! Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@montynorth3009
2 жыл бұрын
Nice one!
@Chikov2
2 жыл бұрын
Another possible solution. Put the origin at A and write the formula for the line CB. Its slope is rise/run = -12/20. And at 0, its value is 12. So it's formula is y = -12/20*x + 12. However at point D, x = y. So you solve x = -12/20*x + 12. And you get 7.5. That is the length of the side of the square.
@PreMath
2 жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome Peter😀 Keep it up 👍
@jaysong3256
2 жыл бұрын
I like that
@inkognito5448
2 жыл бұрын
Same idea. 👍
@pukaman2000
2 жыл бұрын
Point slope form. Solve for x=y. Yeppers.
@simpleminded1uk
2 жыл бұрын
Yes, that's how I did it.
@harikatragadda
2 жыл бұрын
Draw diagonal of the square to the hypotenuse. This divides the big triangle into two smaller triangles, both of altitude a and with bases 12 and 20. Area of the big triangle = ½*12*20 = 120 Sum of areas of the two smaller triangles = ½*12*a + ½*20*a = 16a = 120 Therefore a= 15/2
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome Hari 😀 Keep it up 👍
@susennath6035
2 жыл бұрын
Can clear to me
@jonk3714
2 жыл бұрын
I think an easier way to use the second method is to do 12/20 = (12-a)/a , since the whole triangle is similar to the smaller ones, you dont get a quadratic function and you get to 15/2 with less steps.
@notsoancientpelican
2 жыл бұрын
Always try analysis first. Note that the upper right vertex of the square is a point on the hypotenuse. With origin on the right angle vertex of the triangle, this means line x=y has a common point with hypotenuse line y= -(3/5)x +12. So: x = -(3/5)x +12, and x = 7.5, therefore side of square is 7.5 and area of square is 56.25. voila
@jasonwoods7915
2 жыл бұрын
Another method could be. Find c2. a2 plus b2 equals c2. Cb equals 23.32. Atan(12/20) equal alpha angle is 30.96. Beta angle is 59.04. Point ad is a 45 and hypotenuse green square.
@S2000magician
2 жыл бұрын
My first thought was to write the equation for the hypotenuse: y = 12 − 3/5x. The upper right corner of the square lies on the line y = x, so x = 12 − 3/5x, 8/5x = 12, x = 12(5/8) = 7.5. A = 7.5² = 56.25.
@BebListener
2 жыл бұрын
Hello, many thanks for those great math videos, it is always a pleasure to try a solution... Just here a third way to solve it : tg(bêta) = a / (20-a) = 12 / 20 20.a = 240 - 12.a 32.a = 240 a = 15/2 Easy and quick, no ?
@earthcitizen57
Жыл бұрын
Could you please explain a=xy/x+y. If your purpose is to teach in detail, you should explain how you arrived at this formula or what the theorem is called.
@jupitergoat
Жыл бұрын
A comment deriving xy/x+y was deleted, or I can't find it. Very strange to explain and repeat the simplest details then throw that in when it is not at all obvious and not allow a derivation.
@n.stephan9848
Жыл бұрын
The operation of xy/(x+y) is similar to one used in electrotechnics/electronics, for example calculating the resistance of 2 resistors in parallel, or 2 capacitors in series. Adapting an alternative formula, a can also be calculated this way: a=1/(1/x+1/y) Unfortunately I don't know what either operation is called.
@darrylmunns4946
Жыл бұрын
That is exactly what i thought, as soon as he wrote it. Now i have to go back and look at that and see what i missed in electronics class..
@jp-hh9xq
Жыл бұрын
Interesting. Before I clicked on the video I decided to try to solve the problem real quickly. The first thing I thought was the equation of the line CB would be y=-12/20x + 12. Set x=y (because it's a square). So x = (-12/20)x + 12. Solving for x = 7.5, and thus A = 7.5^2 = 56.25 Which is the right answer and doesn't require any "out of the box" thinking. You're thoughts?
@drpkmath12345
2 жыл бұрын
Hey my friend! You have such an amazing playlist for geometry for sure haha Keep rocking my friend! 👍👍👍
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome my friend 😀 Keep it up 👍
@crustyoldfart
2 жыл бұрын
This problem can be seen as the most elementary one in a collection of favourite problems, the most difficult of which is the ladder/wall/box problem. The " intermediate " problem is to consider a right triangle in which is inscribed a square. Express the side of the square in terms of one of the two angles other than the right angle [ in this case angles alpha and/or beta ]. Using the numbers in the given problem we can show that a/20=tan(beta)/(1+tan(beta)); tan (beta)=12/20. In the classic ladder problem we are given the ratio of the ladder length to the box side [ here the hypotenuse length to a ] and are required to find the other two sides of the triangle. A simple solution using the angle parameter follows which avoids having to solve a 4-power polynomial.
@TheLechers
2 жыл бұрын
How was formula xy/(x+y) realised?
@StaffanSAN
2 жыл бұрын
That’s what I’m looking for in the comments as well!
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@andrewkarsten5268
2 жыл бұрын
Just do the second method but use x and y instead of 20 and 12
@martschkiperov4694
Жыл бұрын
third method: triangle area equals from upper triangle + square + left triangle: a*(12-a)/2+a^2+a*(20-a)/2 = 12*20/2 opening brackets: 6a-a^2/2+a^2+10a-a^2/2= 120 | taking down -a^2/2+a^2-a^2/2 6a+10a= 120 16a=120 => a=120/16 | divide with 8 | = 15/2 required area: a^2 = (15/2)^2 = 225/4 = 50 + 25/4=56,25
@HassanLakiss
2 жыл бұрын
Nice question and nicely done but please explain where you get your formula in your first method. Thank you
@PreMath
2 жыл бұрын
Dear Hassan, second method is the proof of the first method. Thanks for asking.😀 Keep it up 👍
@sharonmarshall3671
Жыл бұрын
I used ratios and similarity and arrived at same answer. Letting x represent shortest side of smallest triangle and y the side of the square, then x:y = 3:5. Then letting x = 3u and y =5u I derived the equation 3u + 5u = 8u =12, hence u = 12/8 or 3/2. Since y =5u, y= 5(3/2) = 15/2 . Area of square = y^2 which is (15/2)^2 or 225/4 ie 56.25.
@saidchaida5431
2 жыл бұрын
Nice problem! The second method is simply the proof of the first method. I like your channel (I am subscribed) brings back good memories
@bfelten1
2 жыл бұрын
Exactly. It becomes obvious if you don't insert numbers too early. Never do that if you want top scores, it's much less elegant. :)
@PreMath
2 жыл бұрын
Very true! Thank you for your feedback! Cheers! You are awesome Said 😀 Keep it up 👍 Love and prayers from the USA!
@اممدنحمظ
2 жыл бұрын
شكرا جزيلا لكم . والله يحفظكم ويرعاكم ويحميكم
@tombufford136
Жыл бұрын
Had a quick go at this. I formed three rectangles which gives your formula, though I did not go this far. Thank you for your Video.
@zsoltszigeti758
2 жыл бұрын
I used coordinate geometry: the diagonal of the square is x=y, the hypotenuse of the triangle is y=12-12x/20; the result is x=15/2
@PreMath
2 жыл бұрын
Excellent approach! Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@qua7771
2 жыл бұрын
How did you come to the conclusion to use A=XY/(X+Y)?
@Elizabeth-qq8rl
2 жыл бұрын
.
@nirupamasingh2948
2 жыл бұрын
Thank you for two methods of solving this question
@PreMath
2 жыл бұрын
You are very welcome. Glad to hear that! Thank you for your feedback! Cheers! You are awesome Neru 😀 Keep it up 👍
@hutchings003
2 жыл бұрын
A quicker way is to find the formula for the hypotenuse line and then set y=x since it is a square (the origin has to be at the right angle). Y=(-12/20)x+12 Set y=x and solve for x gives you 7.5
@victorsoto2188
2 жыл бұрын
Thank you for explaining the formulas. I have one question, suppose you have a smaller square in the triangle would the formula still work or does the formula work for a perfect largest square only. Peace
@NigelRCharman
Жыл бұрын
A quick solution i have found is as follows: draw a diagonal across the square, bottom left to top right. That makes four triangle. The two on the left hand side have a combined base of 12 and height of a, so area of 1/2 × 12 x a. The lower two have an area of 1/2 x 20 x a. The whole triangle has an area of 1/2 x 12 x 20. So (1/2 x 12 x a) + (1/2 x 20 x a) = 1/2 x 12 x 20. 32a = 240 A= 240/32
@devondevon4366
2 жыл бұрын
label the square x .hence the top of the square is 12-x and the bottom of the square is 20-x. Remove the square, leaving rectangle 12-x and x and another rectangle 20-x and x. rotate the 12-x by rectangle such that its x side fits the x side of the 20-x by x by x rectangle. The new rectangle, formed by the two rectangles, has height x and base 12-x + 20-x. Its area is 12x-x^2/2 + 20x-x^2/2 = 6x-0.5x^2 + 10x-0.5x^2= 16x-x^2. But the area of the entire figure is 16x-x^2 + (x^2)=16x=120 16x=120 x=7.5 area=7.5x7.5 =56.25
@sankaranarayanankm7273
Жыл бұрын
Traiangle ABC & Triangle EBD are similar. Hence AC/AB= ED/EB. 12/20= x/(20-x) 3/5= x/(20-x) which gives x=60/8=7.5
@michaelstahl1515
2 жыл бұрын
You did a great job as ever. But I found CD : FD = CA : AB . It`s equal to ( 12 - a ) : a = 12 : 20 . I got a = 7, 5 and a * a = 56, 25 Squareuntis. I hope you accept and correkt my faults in English . I´m learning ( not in Math`s) .I like you `re chanell !
@nivan231
2 жыл бұрын
Hello Sir.. in the first method, can u just help me know what's the theorem name which gets us the value of a=xy/(x+y)? Thats a perfect one, just wanted to know theorem name or formulae name.
@n.stephan9848
Жыл бұрын
Unfortunately I don't know what it's called. It is however also used in electrotechnics/electronics; for example in calculating the resistance of 2 resistors in parallel, or the capacitance of 2 capacitors in series. I was also thought another formula that could be used instead, adapting that gives you this: a=1/(1/x+1/y)
@nivan231
Жыл бұрын
@@n.stephan9848 no issues Sir.. and thanks for the information 👍
@davidstecchi9501
9 ай бұрын
i you are going to use similar triangles to solve for the side length, why not use triangle ABC and triangle EBD eliminating the need to take a square root?
@williamwingo4740
Жыл бұрын
After fooling around with Pythagoras for a few minutes to no avail, I came up with this: Let a = the side of the square. Area of the entire triangle = (12)(20)/2 = 120; Area of the smaller upper triangle = (a)(12 - a)/2 = (12a - a^2)/2 = 6a - (a^2)/2; Area of the larger right-hand triangle = (a)(20 - a)/2 = (20a - a^2)/2 = 10a - (a^2)/2; Area of the entire triangle = the sum of these three: 120 = a^2 {square} + (6x - (a^2)/2) {upper triangle} + (10a - (a^2)/2) {right-hand triangle}; collecting terms: 120 = a^2 + 16a - (a^2)/2) - (a^2)/2) = a^2 + 16a -- 2[(a^2)/2] = a^2 + 16a -- a^2; the a^2 terms subtract out, and 16a = 120; a = 120/16 = 7.5; and the area of the square = a^2 = (7.5)^2 = 56.25. Cheers. 🤠
@sergeynite2306
Жыл бұрын
The simplest method is to see the large triangle as half of the rectangle. Then the square of this rectangle is 12*20 or it is the sum of its parts (12-a)*a + (20-a)*a + 2*a^2 = 12a - a^2 + 20a - a^2 + 2*a^2 = 32a. Therefore 32a = 240 or a = 15/2.
@furzaanullah8114
2 жыл бұрын
Thank you for such good question. It is helping me improve day-by-day. Can you make a video on trigonometry please.
@PreMath
2 жыл бұрын
You are very welcome. Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍 Love and prayers from the USA!
@ihti20
Жыл бұрын
Draw diagonal of the square, you'll cut triangle into two with areas 10a and 6a. Thence 16a=120. a = 15/2, A=225/4. It's the easiest solution.
@michaelstahl1515
2 жыл бұрын
That was the same solution I choosed. Using the second theorem of simular threeangles . (12 - x) / x = 12 / 20 !
@gydglt4538
Жыл бұрын
The straightforward solution is to use the équation y=ax+b for the hypothenus.. y= -3/5x+12. Then look for the value "a" where x=y in that équation.. a= -3/5 a +12 .... a=15/2
@spiderjump
2 жыл бұрын
Let side of square be 3 a Then by similar triangles base of larger triangle = 5a Hence 8a=20 3a= 7.5 Area = (7.5)square
@nevermind-wp3bf
Жыл бұрын
We can use Thales becouse we've got 2 right triangles which are alike or resamble each other ( CAB and DEB becouse they have got 2 equal angles, and DE is parallel with AC) and if we note the side of the square with "x", according with Thales theorem we will have the following report, from those 2 alike triangles: DE/CA = EB/AB; But, DE = x; CA = 12; EB = 20 - x and AB = 20, Therefore, when we make the substitution in the above report, we will get: x/12 = (20-x)/20 => 12 * (20 - x) = 20x => 240 - 12x = 20x => 20x + 12x = 240 => 32x = 240 => x = 240/32 => x = 7,5 The aria of the square = x^2 x^2 = 7,5^2 = 56,25
@philipkudrna5643
2 жыл бұрын
Before watching: similar triangles lead to a/(12-a)=(20-a)/a. This leads to a=7.5 and the area being 56.25 square units. After watching: the „shortcut“ is actually the same as the second method, as the second method is the proof for the formula applied. (a in the end is 12*20/(12+20) which is exactly the formula applied in the beginning…)
@PreMath
2 жыл бұрын
Excellent Philip! Thanks for sharing! Cheers! You are awesome 😀 Keep it up 👍
@shapourmehrkar-asl1845
2 жыл бұрын
All the three triangles are similar. This mean the ratio of the shorter side to longer side is 12/20 or 0.6. The each side of square is a summing to be a. The length 12 is equal to a + 0.5a. This means a=12/1.6=7.5 Area is 7.5x7.5=56.25
@SeverSpanulescu
Жыл бұрын
For 10 seconds: the area of the triangle ABC is 12x20/2=120. It equals the of the area of the triangle ADB which is 20a/2, plus ADC which is 12a/2. Hence 10a+6a=120, a=15/2. Its square is 225/4.
@Bilbobaggiins.0
2 жыл бұрын
we are lucky because we find and we suscribe Sir Channel .un susciber dont know the importance of this channel . sir video increase our mind set and build logical thinking which is helping us to solve difficult questions easily
@PreMath
2 жыл бұрын
Wow, thanks Nilesh dear. Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍 Love and prayers from the USA!
@romananufriev3909
2 жыл бұрын
The area of green square is a^2. From the other side this area is area of big triangle 1/2(12*20) minus areas of two small triangles 1/2((12-a)a) and 1/2((20-a)a). So, a^2=1/2(12*20)-1/2(((12-a)a)- 1/2((20-a)a). The answer is the same
@JohnAlcaraz
2 жыл бұрын
I solved it using similar triangles also, but noted that triangles CFD and CAB were simiilar. The resulting math was a little easier.
@PreMath
2 жыл бұрын
Excellent! Thank you for sharing! Cheers! You are awesome John 😀 Keep it up 👍
@syphaxjuba8420
2 жыл бұрын
thank you sire , voilà je ne comprend pas l'anglais mais c'est formidable de découvrir des théorème simple , qui sont utiles dans la vie courante , et bon courage
@HR-yd5ib
Жыл бұрын
so you go into lengths to explain that the area of a square is computed as a * a, but then you drop the equation x*y/(x+y) out of nowhere. Great stuff!
@patk5148
Жыл бұрын
l m not so good at some of these triangle and circle problems, but l am improving a bit - need some refreshing! Trig is fine with me. Method: The big triangle is comprises of 2 triangles and a square inside. Area of the big Tri.... is equal to the triangle(1) + square + triangle(2) Aim is to calculate the X- value of the square sides. Therefore: 12x20/2 = 240/2 = 120sq Units(Big Triangle) ... 120 = x(12 - x)/2 + x(20 - x)/2 + x^2 32x/2 = 120, 32x = 240, x value= 7.5 Units A of square = 7.5 x 7.5 = 56.25 sq U....
@AnonimityAssured
2 жыл бұрын
Isn't it amazing that the formula for _a_ is essentially the same as that for the side-length of the square in the video posted on Oct 3, 2021, that for _h_ in the video posted on Sep 24, 2021, and that for MN in the video posted on Jun 3, 2021? Well, perhaps it's not so surprising. They are very similar problems in many ways. Perhaps some people might like to derive a formula for the following: Two circles of diameter d₁ and d₂ are touching at point P. If _x_ represents the shortest distance between P and either of the common tangents to the circles that do not pass through P, what is the value of _x_ in terms of d₁ and d₂? What would be the formula in terms of the two radii, r₁ and r₂?
@nickcellino1503
Жыл бұрын
Since the total area of 120 (12/2 x 20) is equal to the sum of the two interior triangles plus the area of the square, we can determine the area of the square by determining the areas of the two triangles. The area of the square is a². The area of the larger interior triangle is (a)(20-a)/2 = (20a-a²)/2. The area of the smaller interior triangle is (a)(12-a)/2 = (12a-a²)/2. Now add the 3 components. a² + (20a-a²)/2 + (12a-a²)/2 = 120 Simplify by multiplying by 2. 2a² + 20a -a² + 12a -a² = 240 32a = 240 a = 7.5 so the area of the square is (7.5)² = 56.25. However, finding the answer in 10 seconds as promoted is extremely difficult.
@HappyFamilyOnline
2 жыл бұрын
Wow amazing explanation👍 Thank you so much😊😊
@ranymattar185
2 жыл бұрын
I am confused, why is xy/x+y equal to a?
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@clementmakamo4557
2 жыл бұрын
Me too
@JLvatron
2 жыл бұрын
I used the 2nd method; which if you used variables X & Y instead of 20 & 12, would prove the formula in the 1st method.
@PreMath
2 жыл бұрын
Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome JL😀 Keep it up 👍
@satyamreddy9714
2 жыл бұрын
Second method is and clear to understand. Good explanation.tq
@abuyazid3762
2 жыл бұрын
The two small triangles are alike a/(12-a) = (20-a)/a And solving the equation a=7.5
@rivivuel8188
2 жыл бұрын
I would've done it a bit different: 1.find hypetonuse 2. calculate area of triangle 3. Substitute area and hypotenuse as the base into formula for calculating triangle to get the height 4. Use the height as the diagonal of the square 5. Square is a 45-45-90 triangle so find sides 6. Multiply sides to get area of square. Done!
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@andrewkarsten5268
2 жыл бұрын
The problem is the height is not the diagonal of the square. The diagonal isn’t perpendicular to the hypotenuse, which means we can’t apply ½(base)(height)=area
@Fgarber1
Жыл бұрын
I did it similarly, but even easier. No need for hypotenuse! The Square is the area of the whole triangle minus the area of the two smaller triangles. A right triangle is Area = 1/2bh. For each of the smaller triangles, one of the sides is a and the other is (constant-a) So you get a^2 = (12*20*0.5) - (a * (20-a) * 0.5) - (a * (12-a) * .05). Expand that out and combine like terms and you get a^2 = 120-16a + a^2, which further reduces down to a = 15/2, so the area of the square is (15/2) ^ 2 or 56.25. No need to remember any Geometry principles, it's all algebra.
@schrodingerzcat13
Жыл бұрын
Area of big triangle = area of two small triangles + area of square 1/2 (20x12) = 1/2[(20-a)a] + 1/2[(12-a)a] + a’2 = solves for a directly, then find a’square.
@hazimec
2 жыл бұрын
why not use more simple analysis , from triangle symmetry that is (12-a)/a=12/20 ; (12/a-1)=12/20 ; 12/a=(2/20+1) ;so a=7.5
@FaixaPretanoENEM
2 жыл бұрын
Step by step as usual! Best math teacher ever! Thanks!
@242math
2 жыл бұрын
used the second method, love this area problem, thanks for the challenge
@pronkow
2 жыл бұрын
a can be determined in a much easier way. The area of the triangle ABC: A=0.5*20*12=120 The triangle ABD has the area A1=0.5*20*a=10a Triangle ADC A2=0.5*12*a=6a Now A=A1+A2, so 120=10a + 6a = 16a a=120/16=7.5 Green area = 7.5²=56.25 🤓
@Viesto1980
2 жыл бұрын
Let a to be lenght of side of the green square. (12-a)/a=12/20 12a=240-20a 32a=240 a=7,5 a^2=56,25
@franksamona2491
Жыл бұрын
Where does this formula come from? a=(xy/x+y). I've never heard of it!!
@quigonkenny
5 ай бұрын
Quick method: Look at the ratios of the two sides: 12 and 20. What relation is the smaller number to the larger? 12 is 3/5 of 20. Look at the upper triangle. You can see that the length of the left side of rhe triangle plus the base (the side of the square) equals 12. The ratio between the two sides is, as with the larger triangle, 3 to 5. Add those two numbers and divide into 12. 12/8 = 1.5. That's what each "chunk" of side length is. The left side is 3 chunks (3•1.5) or 4.5. The bottom (and thus square side length) is 5•1.5 or 7.5. 7.5² = 56.25 It works the other way as well if you find that easier. 20/8 = 2.5, so the side lengths of the lower triangle are 7.5 (square) and 12.5 (bottom). The description of the method is a lot less quick than the method itself. Once you do it a few times it'll be pretty easy to do so wuickly in your head.
@mustafalale980
2 жыл бұрын
hi . there is more simple solution. draw a line from A to D . A(ADC) + A ( ADB ) = ( 12* a/2 ) + ( 20* a/2) = A (ABC ) ... 16a=120 and a = 15/2 and square Area = a^2 thsat is all :)
@cenkalmastal
2 жыл бұрын
Escrevi errado o quadrado da área ao calcular, agora estou digitando corretamente! a/12 = (12-a)/20; => 20a = 144-12a; => 32a = 144; => 2a = 9; => a = 9/2; => a = 4,5 br => b = (12-a); => b = (12-4,5); => b = 7,5 br; => s(ABCD) = b²; => s(ABCD) = 56,25 br²; Será em forma de resposta!
@zsus1
Жыл бұрын
good one..thank you
@fahimelabidi7447
2 жыл бұрын
Easy method, assume x is square length, use theorm of TALES, then: a/12=(20-a)/20. That's it! It took me 4 seconds!
@GaryTugan
2 жыл бұрын
Your first equation …. Ya just Poof, threw it in there. It is probably way more helpful to start with the hypotenuse being a line and writing the equation of the line for it: y= Mx+b where M = -12/20 = slope. Gives: y = -12/20 x + 12 …. Then plug in for the point on the line where the square intercepts (a,a)… a= (-12/20)a+12 (32/20)a = 12 Therefore: a = 12*(20/32)=7.5 Then use a^2= 7.5^2
@siddhantofpremath1788
2 жыл бұрын
Sir you are not only mathematician but also mathemagician....!😊
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍 Love and prayers from the USA!
@siddhantofpremath1788
2 жыл бұрын
Sir can you pls provide me with your gmail because I want to know about some study and education policies and criteria in USA...
@PreMath
2 жыл бұрын
@@siddhantofpremath1788 Hello dear, here is the email: premathchannel@gmail.com
@tulasikolluru3618
Жыл бұрын
Sir 2nd method is fine, but how do we get a=xy/x+y)
@DARK____SIDE
Жыл бұрын
sir you would have explained from where that xy/x+y came from.🤔
@gaskellr44
2 жыл бұрын
Where does a = XY/(X + Y) come from with full derivation please ?
@mustafizrahman2822
2 жыл бұрын
It is fully impossible for me to solve it in 10 seconds. But I have solved it in 1 minute 56 seconds, that is about 2 minutes. However, I have used cartesian co-ordinate and my answer is 56.25 square units.
@Trr1fstud
2 жыл бұрын
U r genius bro keep it up..,,..
@mustafizrahman2822
2 жыл бұрын
@@Trr1fstud I am not genius.
@PreMath
2 жыл бұрын
Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@yoyobangz2000
2 жыл бұрын
Why not just calculate total area of large triangle use a as your variable and total area = 1/2(20-a)(a)[medium triangle]+1/2(12-a)(a)[small triangle]+(a^2)[area of square]. The a^2 cancel out and you end up with 16a=120 or a =15/2
@DARK____SIDE
Жыл бұрын
actually we could have divide 15/2 which is 7.5 and appky the formula of ar of square. but n8ce explaination sir❤
@luizverdecanna8023
2 жыл бұрын
What formula ? out of the blue ?
@colinhannigan9599
Жыл бұрын
I have watched a few of your explainatory videos mostly interesting and informative, thank you. However this one a bit irksome in 2 respects; a) the first formulae you used seemed to appear from the ether b) 10 seconds? Yeah, right! It seems a bit of a cheap headliner to generate views.
@Martin-vu5fl
2 жыл бұрын
The fomula a = (xy)/(x+y) , I am sure he is right, but why would that be true? Is this a formula?
@PreMath
2 жыл бұрын
Second method is the proof of that!
@dineshmalla3651
Жыл бұрын
Another method is to use similar triangle properties as ABC Triangle is similar to DEB
@ruilongsheng2845
Жыл бұрын
12-x/x=x/20-x, 240=32x, x=7.5, area=7.5^2
@leejk9884
Жыл бұрын
There is a way to find the area of a square(rectangle) without any formula. Let D be the vertex of the square that intersects the opposite side of the triangle, and let the length of segment AB of the triangle be 12 and the length of segment BC be 20. The area of triangle ABC is 12*20/2=240/2=120, and the area of triangle ADB and triangle BDC is divided by the ratio 12/(12+20) : 20/(12+20). That is, the area of triangle ADB is 120*12/(12+20) = 45, and the area of triangle BDC is 120*20/(12+20) = 75. Triangle ADB is divided into half of the square and remainder of the triangle, so the area of the half of the square is 45*20/(12+20) = 225/8. Therefore, the area of the square we want to find is 2*225/8=225/4. Triangle BDC is also divided into half of the square and remainder of the triangle. The area of the half of the square is 75*12/(12+20) = 225/8.
@ion4926
2 жыл бұрын
Thank you sir
@PreMath
2 жыл бұрын
You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@LarzB
2 жыл бұрын
That was no 10 seconds and the first method is derived in the same way as the second method so they are similar. A sightly different way would be the area of the big triangle minutes the 2 small ones with a as variable and have that equal to a². Then the answer a = 120/16 is also the result
@mryip06
2 жыл бұрын
let x be the length of the square 12x/2 + 20x/2 = 20•12/2 16x = 120 x = 15/2 required area = x² = 225/4
@PreMath
2 жыл бұрын
Excellent! Thank you for sharing! Cheers! You are awesome Felix 😀 Keep it up 👍
@theoyanto
Жыл бұрын
Yeah nice, i used the correct method, like triangles, but got wrong answer, so i think i just got my arithmetic wrong, I used the similarity between tha large outer triangle and the triangle on the right, the mid sized triangle i thought they were similar, just need more practice, still enjoyed it though. Oh yeah, didn't know sbout the xy/x+y that's a cool trick I'll remember that one
@sigmamaleslogokijalegi6683
2 жыл бұрын
I didn't had any idea abt the step 1 completely, i only solved through similar triangle properties. I m bit new mathematics
@PreMath
2 жыл бұрын
No worries. Thank you for your feedback! Cheers! You are awesome 😀 Keep it up 👍
@tombufford136
Жыл бұрын
So we have a * x + a * y = x * y. rearranging x + y = x * y/ a and then a = x * y / ( x + y)
@michaeldragner4670
2 жыл бұрын
Method 3: The equation of the hypotenuse is y = - 3/5x +12. Let put the horisontal side of the square as x. Therefor, the vertical side is -3/5x +12. Since we have a square it implies x = -3/5x + 12. Therefor x = 15/2
@andrewkarsten5268
2 жыл бұрын
Hey everyone, If you’re wondering how the formula for a was derive in the first method, just go through the second method but use x and y instead of 20 and 12. Should make it clear then
@meofamily4
Жыл бұрын
Thank you.
@Knulppage
2 жыл бұрын
10 seconds....video is 8 min. These videos have me hooked.
@dennishollifield381
Жыл бұрын
Where did that formula come from?
@sm1gameplay565
2 жыл бұрын
1:48 how did we get a = (xy)÷(x+y) Somebody help
@PreMath
2 жыл бұрын
First method is just the application of second method. Thanks for asking. Keep it up 👍
@sm1gameplay565
2 жыл бұрын
@@PreMath ohk😀
@francedaledano8751
2 жыл бұрын
can somebody explain to me why do we divide and how the first equation works
@adgf1x
Жыл бұрын
As.of green shaded square=(7.5)^2=56.25 sq unit.
@davidguy9197
Жыл бұрын
superbe! une gymnastique mentale oubliée de ne pas pratiquer
@vanessawelles4760
2 жыл бұрын
tan theta= 12/20 = 0.6 therefor 0.6 = (12-x)/x x= 7.5 green area = 7.5^2= 56.25 done ! now wasn't that a lot easier?
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