The area of a circle inscribed in an equilateral triangle is 154 cm2. Find the perimeter of the triangle :

Answer: Option D

Radius of incircle $$=\frac{a}{2\sqrt{3}}$$
Area of incircle $$=\left(\frac{\pi \times a^2}{12}\right)c{m}^2$$
$$\begin{array}{rl}& \therefore \frac{\pi a^2}{12}=154\\ & \Rightarrow a^2=\frac{154\times 12\times 7}{22}\\ & \Rightarrow a=14\sqrt{3}\end{array}$$
∴ Perimeter of the triangle :
$$\begin{array}{rl}& =\left(3\times 14\sqrt{3}\right)cm\\ & =\left(42\times 1.732\right)cm\\ & =72.7cm(\text{approx})\end{array}$$