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

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KollegeApply · Accepted Answer

sqrt(pi): 2 Let a be the side of the square. We know: Area of a square = a2 Let r be the radius of the circle. We know: Area of a circle=pi"r"^2 Because the area of the square is the same as the area of the circle, we have: a2 = $\pi$r2 => "r"^2/"a"^2 = 1/pi =>"r"/"a" = 1/sqrt(pi) $\therefore$ Ratio of their perimeters `=(2pi"r")/(4"a") ["Because perimeter of the circle is 2$\pi$r and permeter" "of the square is 4"a"] =(pi"r")/(2"a") =pi/2xx"r"/"a" =pi/2xx1/sqrt(pi) ["Since" "r"/"a" = 1/sqrt(pi)] =sqrt(pi)/2 = sqrt(pi) : 2`

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