If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

Question

Philoid · Accepted Answer

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

We are given that Perimeter of a circle = Perimeter of a square

⇒ 2πr = 4a

⇒ a = πr/2

Area of the circle = r² and Area of the square = a²

Now, Ratio of their areas = (Area of circle)/(Area of square)

=

= 4/π = [4/(22/7)] = 14/11