LUANDATO wrote:If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to?
A. 3/2
B. 4/3
C. 3/4
D. 2/3
E. 1/2
Perimeter of a square =
4s.
Circumference of a circle = 2πr ≈
6r.
To make the math easier, let the perimeter of the square and the circumference of the circle = the LCM of the values in blue = 12.
Square: 4s = 12, implying that s=3
Area = s²= 3² = 9.
Circle: 6r = 12, implying that r=2
Area = πr² = π(2²) ≈ 3*4 = 12.
Resulting ratio:
(square area)/(circle area) = 9/12 = 3/4.
The correct answer is
C.
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