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# Find the lengths of the sides of a triangle whose perimeter is 12 cm and the lengths of the sides are in the ratio $3:2:4$.

**Given:**

Perimeter of the triangle $=12\ cm$.

Lengths of the sides are in the ratio $3:2:4$.**To do:**

We have to find the lengths of the sides of the triangle.**Solution:**

Let the sides of the triangle be $3x, 2x$ and $4x$.

This implies,

$3x+2x+4x=12\ cm$

$9x=12\ cm$

$x=\frac{12}{9}\ cm$

$x=\frac{4}{3}\ cm$

Therefore,

$3x=3\times\frac{4}{3}\ cm=4\ cm$

$2x=2\times\frac{4}{3}\ cm=\frac{8}{3}\ cm$

$4x=4\times\frac{4}{3}\ cm=\frac{16}{3}\ cm$

**The lengths of the sides of the given triangle are $4\ cm, \frac{8}{3}\ cm$ and $\frac{16}{3}\ cm$.**

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