Let the length of the side of the square be a

Let the radius if circle be r

Area of a square = a²

Area of circle = πr²

Area of a square = Area of a circle

a² = πr²

a = √π × r

Perimeter of circle = 2πr

Perimeter of square = 4a

= 4√π r

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