The sides of a triangle are in ratio of 1/2:1/3:1/4 . If the perimeter is 52 cm, then the length of the smallest side is :

Answer: Option D

Ratio of sides = $$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$$   = 6 : 4 : 3
Perimeter = 52 cm
So, sides are :
$$\begin{array}{rl}& \left(52\times \frac{6}{13}\right)cm\\ & \left(52\times \frac{4}{13}\right)cm\&\\ & \left(52\times \frac{3}{13}\right)cm\end{array}$$
So, a = 24 cm, b = 16 cm, and c = 12 cm
∴ Length of smallest side = 12 cm