The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 156cm. What is the length of the long side?

Question: The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 156cm. What is the length of the long side?

Solution:
Ratio of sides = 1/2 : 1/3 : 1/4
= (1/2) × 12 : (1/3) × 12 : (1/4) × 12
= 6 : 4 : 3

Let the side be =6x, 4x and 3x

Then,
6x + 4x + 3x = 156
⇒ 13x = 156
⇒ x = 12

Longest side = 6x = 6 × 12 = 72 cm