Question

Question 5
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

Let radius of circle be r and side of square be a.

According to the given condition,

Perimeter of a circle = Perimeter of a square

$2\pi r=4a\Rightarrow =\frac{\pi r}{2}$

Now, $\frac{Areaofcircle}{Areaofsquare}$

$=\frac{\pi r^2}{(a{)}^2}=\frac{\pi r^2}{{\left(\frac{\pi r}{2}\right)}^2}$

$=\frac{\pi r^2}{\frac{{\pi }^2{r}^2}{4}}=\frac{4}{\pi }=\frac{4}{\frac{22}{7}}$

$=\frac{28}{22}=\frac{14}{11}$