If the perimeter of square region S and the perimeter of...

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

The OA is C.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We have

The perimeter of square region S = 4a; where a = side of the square S
The perimeter of circular region C = 2Ï€r; where r = radius of circular region C

=> 4a = 2Ï€r

a = πr/2

The area of square region S = a^2 = (πr/2)^2 = π^2*r^2/4
The area of circular region C = πr^2

The ratio of the area of S to the area of C = [π^2*r^2/4] / [πr^2] = π/4 = 22/7*4 = 11/14 = ~12/15 = ~4/5. The closest to 4/5 is 3/4.

The correct answer: C

Hope this helps!

-Jay
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Hi LUANDATO,

We're told that the perimeter of square region S and the perimeter of circular region C are EQUAL. We're asked to find the answer that is closest to the ratio of the area of S to the area of C. This question can be solved by TESTing VALUES.

IF....
Perimeter of the Square = 8, then the side length = 2 and the area = (2)(2) = 4

Circumference of the Circle = 8...

8 = 2(pi)(R)
4 = (pi)(R)
4/pi = R
Area = (pi)(R^2) = (pi)(4/pi)^2 = 16/pi = about 16/3 = about 5

(Area of S):(Area of C) = about 4:5. The closest answer is 3/4.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich