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

Let the length of the side of the square be a

Let the radius if circle be r

Perimeter of circle = 2πr

Perimeter of square = 4a

Perimeter of circle = Perimeter of square

⇒ 2πr = 4a

a = π × r/2

Area of a square = a^{2}

Area of circle = πr^{2}

Ratio of area of square to circle = π: 4

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