Question

The sides of a triangle are in the 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

Answer 1

Answer: (D)

$12$ cm

Given Ratio $=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

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

Perimeter of triangle $=$ sum of all sides

$52=\frac{x}{2}+\frac{x}{3}+\frac{x}{4}$

On solving we get, $x=48$

So, Sides are $\frac{x}{2}=\frac{48}{2}=24$ cm

$\frac{x}{3}=\frac{48}{3}=16$ cm

$\frac{x}{4}=\frac{48}{4}=12$ cm

So, the length of the shortest side is $12$ cm.