The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle?

Start with the area of the square.

Let s = side of square.

So, A = s^2.

A circle has a circumference.

C = 2πr

Perimeter of square = area of circle.

4s = 2πr

Solving for r, we get

4s/2π = r

2s/π = r

Ratio:

Area of square : area of circle

s^2 = πr^2

Above we solved for r. So, plug it in.

s^2 : π (2s/π) ^2

s^2 : π (4s^2) / π^2

(s^2) / (4s^2) / π

(s^2) * π / (4s^2)

Answer: π/4