If the areas of a circle and a square are equal then the ratio of their perimeters is-

Question: If the areas of a circle and a square are equal then the ratio of their perimeters is-

Solution:
Let the length of each side of the square = a cm and radius of the circle = r cm.
Given that,
area of square = area of circle
⇒ a² = πr²
⇒ a = r√π​

∴ Required ratio = 2πr​/4a
= ​​2πr​/4r√π
= √π/2
= √π ​: 2