Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

Answer 1

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.

Explanation:

Let circle radius = r and square side = a.

Equal perimeters give 2πr = 4a ⇒ `a = (πr)/2`.

Area ratio (circle : square) = `(πr^2)/a^2` 

= `(πr^2)/((π^2r^2)/4)` 

= `4/π` 

Using `π = 22/7`, 

`4/π = 4/(22/7)` 

= `28/22`

= `14/11`