The area of a square is the same as the area of a circle. Their perimeters are in the ratio

Let the length of the side of the square be a

Let the radius if circle be r

Area of a square = a^{2}

Area of circle = πr^{2}

Area of a square = Area of a circle

a^{2} = πr^{2}

a = √π × r

Perimeter of circle = 2πr

Perimeter of square = 4a

= 4√π r

Ratio of perimeter of circle and square = √π : 2

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