Question

If the perimeter of a circle is equal to that of a square , then the ratio of their areas is
(a) $22:7$ (b) $14:11$ (c) $7:22$ (d) $11:14$

Answer 1

Let radius of given circle be $r$ units. and length of side be $a$ units.
Given condition: Perimeter of a circle $=$ Perimeter of a square
$2\pi r=4a$
$\Rightarrow r=\frac{4a}{2\pi }$
$\therefore r=\frac{2a}{\pi }$
Now area of the circle $=\pi r^2$
$=\pi (\frac{2a}{\pi }{)}^2$
$=\frac{4a^2}{\pi }$
Area of the square$=a^2$
the ratio of area's of circle to the side is $=\frac{4a^2}{\pi }:a^2$
$=\frac{4a^2}{\pi \times a^2}$
$=\frac{4}{\frac{22}{7}}$
$=\frac{4\times 7}{22}$
$=\frac{14}{22}$
$=14:22$
Hence, the required ratio is $14:11.$
Therefore, the correct answer is option (b) ($14:11$)