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# If the sides of a triangle are in the ratio $ 3: 4 : 5 $ and its perimeter is $ 24 \mathrm{~cm} $, find the measure of each side of the triangle.

Given:

The sides of a triangle are in the ratio \( 3: 4 : 5 \) and its perimeter is \( 24 \mathrm{~cm} \).

To do:

We have to find the measure of each side of the triangle.

Solution:

Perimeter of a trinagle of sides $a, b$ and $c$ is $a+b+c$.

Let the sides of the triangle be $3x, 4x$ and $5x$.

This implies,

$3x+4x+5x=144$

$12x=24$

$x=\frac{24}{12}$

$x=2\ cm$

$3x=3(2)=6\ cm$

$4x=4(2)=8\ cm$

$5x=5(2)=10\ cm$

**Therefore, the sides of the triangle are $6\ cm, 8\ cm$ and $10\ cm$.**

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