Question

The length of the sides of a triangle are in the ratio $2:3:4.$ If its perimeter is $225$ units, find the length of the smallest side.

• A. $25$ units
• B. $50$ units
• C. $16$ units
• D. $100$ units

Answer 1

The correct option is B $50$ units

Ratio of the length of the sides of the triangle is $2:3:4.$
So, the measure of the sides can be taken as $2x,3x,$ and $4x.$
Perimeter $=225$ units
So, $2x+3x+4x=225$
$\Rightarrow 9x=225$
Dividing by $9$ on both sides, we get:
$\Rightarrow \frac{9x}{9}=\frac{225}{9}$
$\Rightarrow x=25$
Hence, the length of the smallest side $=2x=2\times 25=50$ units