Solution: I draw a line from O to B and AC = diagonal of rectangle = OB = radius of quarter circle = r = 6. The perimeter of the rectangle is 16, which means: 2*(AO+OC) = 16 |/2 ⟹ AO+OC = 8. Now is: The circumference of the brown area = = 2*π*r/4+PA+AC+CQ = π*r/2+PO-AO+OB+OQ-OC = π*r/2+r-AO+r+r-OC = π*r/2+3r-(AO+OC) = π*r/2+3r-8 = π*6/2+3*6-8 = 3π+10 ≈ 19,4248
@LuisdeBritoCamacho
5 ай бұрын
Hello! 1) Let AB = OC = X 2) Let OA = BC = Y 3) Let OB = R = 6 4) Let 2X + 2Y = 16 ; 2*(X + Y) = 16 ; X + Y = 8 5) X + Y = 8 and X^2 + Y^2 = R^2 ; X^2 + Y^2 = 36 System of Two Equations: a) X + Y = 8 b) X^2 + Y^2 = 36 6) Positive Solutions: 7) X = 4 - sqrt(2) and Y = 4 + sqrt(2) 8) AP = 6 - (4 + sqrt(2)) Linear Units 9) CQ = 6 - (4 - sqrt(2)) Linear Units 10) AC = OB = 6 Linear Units 11) Arc PQ = 2*Pi*R / 4 ; Arc PQ = Pi*6/2 ; 3Pi Linear Units 12) Perimeter = [6 - (4 + sqrt(2)) + 6 - (4 - sqrt(2)) + 6 + (3Pi] Linear Units 13) Perimeter = 6 - 4 - sqrt(2) + 6 - 4 + sqrt(2) + 6 + (3Pi) Linear Units 14) Perimeter = (10 + 3Pi) Linear Units 15) Perimeter ~ 19,425 Linear Units.
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