2010 AMC 8 Problems/Problem 16

Problem

A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?

Solution

Let the side length of the square be $s$ , and let the radius of the circle be $r$ . Thus we have $s^2=r^2\pi$ . Dividing each side by $r^2$ , we get $s^2/r^2=\pi$ . Since $(s/r)^2=s^2/r^2$ , we have $s/r=\sqrt{\pi}\Rightarrow \boxed{B}$

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2010 AMC 8 Problems/Problem 16

Problem

Solution