The area of a triangle is 216 cm2 and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is :

Answer: Option D

Let a = 3x cm, b = 4x and c = 5x
Then, s = 6x
$$\begin{array}{rl}& A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ & =\sqrt{6x\times 3x\times 2x\times x}\\ & =\left(6x^2\right)c{m}^2\\ & \therefore 6x^2=216\\ & \Rightarrow x^2=36\\ & \Rightarrow x=6\end{array}$$
So, a = 18 cm, b = 24 cm and c = 30 cm
Perimeter :
= (18 + 24 + 30) cm
= 72 cm