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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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