Question

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

• A. $9cm$
• B. $10cm$
• C. $11cm$
• D. $12cm$

Answer 1

Answer: (D)

$12cm$

Let the sides of the triangle be x.

Then,

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

$6x+4x+3x=624$

$13x=624$

$x=48$

Then $\frac{x}{2}=24cm$, $\frac{x}{3}=16cm$ and $\frac{x}{4}=12cm$

Hence, $\frac{x}{4}=12cm$ is the smallest side