If the area of a square is same as the area of a circle, then the ratio of their perimeters, in terms of $\pi$, is

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We have given that area of a circle of radius r is equal to the area of a square of side a. $\therefore$ pir^2=a^2 $\therefore$ a=sqrtpir We have to find the ratio of the perimeters of circle and square. `$\therefore$ "perimeter of circle"/"Perimeter oof square"=(2pi r)/(4a)` ..................(1) Now we will substitute a=sqrtpir in equation (1) `$\therefore$ "perimeter of circle"/"Perimeter oof square"=(2pi r)/(4sqrtr) $\therefore$ "perimeter of circle"/"Perimeter oof square"=pi/(2sqrtpi) $\therefore$ "perimeter of circle"/"Perimeter oof square"=sqrtpi/2` Therefore, ratio of their perimeters is sqrtpi:2

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