Question

If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of π, is

(a) π : $\sqrt{3}$

(b) 2 : $\sqrt{\mathrm{\pi }}$

(c) 3 : $\mathrm{\pi }$

(d) $\mathrm{\pi }:\sqrt{2}$

Answer 1

We have given that area of a circle of radius r is equal to the area of a square of side a.

We have to find the ratio of the perimeters of circle and square.

………(1)

Now we will substitute in equation (1).

Therefore, ratio of their perimeters is.

Hence, the correct answer is (b).