# A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100cm, calculate the radius of the circle?

Jul 17, 2018

Radius of the circle color(purple)(= 7 cm

#### Explanation:

Circumference of circle $= \pi d$

Perimeter of square = 4 d#

Given the side of the square and diameter of the circle equal. Let it be ‘d’.

$\therefore \pi d + 4 d = 100 c m$

$d \cdot \left(\pi + 4\right) = 100 c m$

$d = \frac{100}{\pi + 4} \approx 14 c m$

Radius of the circle $r = \frac{d}{2} = \frac{14}{2} = 7 c m$