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

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