Question

If the area 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 radius of circle be 'r' and side of square be 'a'.
Now, $\pi r^2=a^2\frac{r}{a}=\frac{1}{\sqrt{\pi }}$
again,$\frac{2\pi r}{4a}=\frac{\pi r}{2a}=\frac{\pi }{2}\times \frac{1}{\sqrt{\pi }}=\frac{\sqrt{\pi }}{2}$
$\therefore$ Required ratio is $\sqrt{\pi }:2$