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# If the circumference of a circle and the perimeter of a square are equal, then find relationship between radius of the circle and side of the square.

**Given: **Circumference of a circle and the perimeter of a square are equal.

**To do:** To find relationship between radius of the circle and side of the square.

**Solution:**

Let "$r$" be the radius of the circle and "$a$" be the side of the square.

Circumference of the circle$=2\pi r$

Perimeter of the square$=4a$

As given, circumference of a circle and the perimeter of a square are equal.

$\Rightarrow 2\pi r=4a$

$\Rightarrow r=\frac{4a}{2\pi}$

$\Rightarrow r=\frac{2a}{\pi}$

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