Question

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

Answer 1

Given the perimeter of a circle is = to that of the square

P circle = P square

Let r be the radius of the circle & a besides of square, then.

2πr = 4a

[r/a = 4/2π = 2/π]

Now,

Area of a circle / Area of square = πr²/a² = π ( r/a) ²

Using r/a = 2/π , we get

Acircle / Asquare = π (2/π)² = 4/π² * π = 4/π

Hence the ratio of the area of a circle to that of a square is 4/π.

Answer 2

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