Question

If the areas of a circle and a square are equal then the ratio of their perimeters is

• A. $1:1$
• B. $2:\pi$
• C. $\pi :2$
• D. $\sqrt{\pi }:2$

Answer 1

The correct option is D $\sqrt{\pi }:2$

Let the length of each side of square $=a$ cm
and radius of circle $=r$ cm
Then $a^2=\pi r^2\Rightarrow a=r\sqrt{\pi }$

$\therefore$ Required ratio $=\frac{2\pi r}{4a}=\frac{2\pi r}{4r\sqrt{\pi }}=\frac{\sqrt{\pi }}{2}$