Question

If the perimeter of a circle is equal to that of square, then the ratio of their areas is:
(A) $22:7$
(B) $14:11$
(C) $7:22$
(D) $11:14$

Answer 1

The correct option is B: $14:11$

Let the radius of the circle be $r$ and side of square be $a.$
According to the given condition,
The perimeter of a circle $=$ Perimeter of a square [Given]
$2\pi r=4a$

$\Rightarrow a=\frac{\pi r}{2}\dots \dots \dots \left(i\right)$

Now, $\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi r^2}{(a{)}^2}$

$=\frac{\pi r^2}{{\left(\frac{\pi r}{2}\right)}^2}$ [Using $eq.\left(i\right)$]

$=\frac{\pi r^2}{\frac{{\pi }^2{r}^2}{4}}$

$=\frac{4}{\pi }$

$=\frac{4}{\frac{22}{7}}$

$=\frac{28}{22}$

$=\frac{14}{11}$