Comment
Share
Q)

# If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

$\begin{array}{1 1}(A) \; 7:22 \\(B)\;11:14 \\(C)\;22:7 \\(D)\;14:11\end{array}$

Let the radius of the circle be $r$ and side of the square be $a$.
Then, according to question, $2 \pi r=4a=>\large\frac{2 \pi r}{4}=\frac{\pi r}{2}$ Now, ratio of their areas,
$\large\frac{\pi r^2}{\bigg(\Large\frac{\pi r}{2}\bigg)^2}$
$\qquad= \large\frac{\pi r^2 \times 4}{\pi ^2 r^2}$
$\qquad=\frac{14}{11}$
$\qquad= \pi r^2 :a^2$
$\qquad= 14:11$