Question

Given a square and, a circle of the same area. What is larger, the length of the circle or. the perimeter of the square?

Answer 1

$A=L^2=\pi R^2$

$⟹L=\sqrt{\pi }R$

Now, length of circle$=C=2\pi R$

Perimeter of square$=P=4L=4\sqrt{\pi }R$

Now, $\frac{P}{C}=\frac{2}{\sqrt{\pi }}>1$

$⟹P>C$