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1. 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 :

A. 9 cm

B. 10 cm

C. 11 cm

D. 12 cm

Solution:

Ratio of sides =

\frac{1}{2} : \frac{1}{3} : \frac{1}{4}

= 6 : 4 : 3
Perimeter = 52 cm
So, sides are :

\begin{aligned} (52 \times \frac{6}{13}) c m \\ (52 \times \frac{4}{13}) c m & \\ (52 \times \frac{3}{13}) c m \end{aligned}

So, a = 24 cm, b = 16 cm, and c = 12 cm
∴ Length of smallest side = 12 cm

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