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# If the area of a circle is equal to the area of a square, then the ratio of their perimeters is

$\begin{array}{1 1}(A) \; 2:\pi \\(B)\;\sqrt {11} :2 \\(C)\;1:2 \\(D)\; \pi :2 \end{array}$

Let the radius of the circle be $r$ and the side of the square be a.
Then according to the question, $\pi r^2 =a^2=> a = r \sqrt {\pi}$
(i) Now , Ratio of their perimeters $= \large\frac{2 \pi r}{4a}$
Ratio of their perimeters $= \large\frac{\pi r}{2a}$
$\qquad= \large\frac{\pi r}{2r \sqrt {\pi}}$
$\qquad=\large\frac{\sqrt \pi}{2}$
Ratio of their perimeters $= \sqrt {\pi}:2$