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

A. 6 cm

B. 12 cm

C. 36 cm

D. 72 cm

Answer: Option D

Solution(By Examveda Team)

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