The radius of a circle is 20% more than the height of a right-angled triangle. The base of the triangle is 36 cm. If the area of triangle and circle be equal, what will be area of circle ?

Answer: Option A

Let the height of the triangle be x cm
Then, radius of the circle = (120% of x) cm = $$\left(\frac{6x}{5}\right)$$ cm
$$\begin{array}{rl}& \therefore \frac{1}{2}\times 36\times x=\frac{22}{7}\times \frac{6x}{5}\times \frac{6x}{5}\\ & \Rightarrow x=\left(\frac{18\times 7\times 5\times 5}{22\times 6\times 6}\right)cm\end{array}$$
So, radius of the circle :
$$\begin{array}{rl}& =\left[\frac{6}{5}\times \left(\frac{18\times 7\times 5\times 5}{22\times 6\times 6}\right)\right]cm\\ & =\left(\frac{105}{22}\right)cm\end{array}$$
∴ Area of the circle :
$$\begin{array}{rl}& =\left(\frac{22}{7}\times \frac{105}{22}\times \frac{105}{22}\right)c{m}^2\\ & =\left(\frac{1575}{22}\right)c{m}^2\\ & =71.6c{m}^2\approx 72c{m}^2\end{array}$$