Question

What will be the ratio of perimeters of a square and a circle if their areas are equal?

Answer 1

Let the side of the square be a and the radius of the circle be r.

Given that the areas are equal.

$a^2=\pi r^2$

$\therefore \frac{a}{r}=\sqrt{\pi }$

It is required to determine the ratio of the perimeter of the square to that of the circle.

$\frac{4a}{2\pi r}$

$=\frac{2}{\pi }\frac{a}{r}=\frac{2}{\pi }\sqrt{\pi }$

$=\frac{2}{\sqrt{\pi }}$