Question

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

• A. 11 cm
• B. 12 cm
• C. 13 cm
• D. 14 cm

Answer 1

The correct option is B 12 cm

Let three sides of the triangle be $\frac{1}{2}x,\frac{1}{3}x,\frac{1}{4}x$

Given $\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=52\Rightarrow \frac{6x+4x+3x}{12}\Rightarrow 13x=52\times 12\Rightarrow \frac{52\times 12}{13}=48$

$\therefore$ The smallest side =$\frac{1}{4}\times 48=12$ cm