In a $\triangle ABC, D, E$ and $F$ are respectively, the mid-points of $BC, CA$ and $AB$. If the lengths of sides $AB, BC$ and $CA$ are $7\ cm, 8\ cm$ and $9\ cm$, respectively, find the perimeter of $\triangle DEF$.

Given:

In a $\triangle ABC, D, E$ and $F$ are respectively, the mid-points of $BC, CA$ and $AB$.

The lengths of sides $AB, BC$ and $CA$ are $7\ cm, 8\ cm$ and $9\ cm$, respectively.

To do:

We have to find the perimeter of $\triangle DEF$.

Solution:

$D$ and $E$ are the midpoints of $BC$ and $CA$.

This implies,

$DE \parallel AB$

$DE =\frac{1}{2}AB$

$=\frac{1}{2}\times7$

$= 3.5\ cm$
Similarly,
$EF=\frac{1}{2}BC$

$=\frac{1}{2} \times 8$

$=4\ cm$

$FD=\frac{1}{2}AC$

$=\frac{1}{2} \times 9$

$=4.5\ cm$

Therefore,

Perimeter of $\triangle DEF=3.5+4+4.5$

$=12\ cm$

The perimeter of $\triangle DEF$ is $12\ cm$.

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Updated on: 10-Oct-2022

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