In the figure, $M, N$ and $P$ are the mid points of $AB, AC$ and $BC$ respectively. If $MN = 3\ cm, NP = 3.5\ cm$ and $MP = 2.5\ cm$, calculate $BC, AB$ and $AC$.
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Given:

In the figure, $M, N$ and $P$ are the mid points of $AB, AC$ and $BC$ respectively.

$MN = 3\ cm, NP = 3.5\ cm$ and $MP = 2.5\ cm$.

To do:

We have to calculate $BC, AB$ and $AC$.

Solution:

$\mathrm{MN}=3 \mathrm{~cm}, \mathrm{NP}=3.5 \mathrm{~cm}, \mathrm{MP}=2.5 \mathrm{~cm}$

$\mathrm{M}$ and $\mathrm{N}$ are the mid points of $\mathrm{AB}$ and $\mathrm{AC}$

This implies,

$\mathrm{MN} \parallel \mathrm{BC}$ and $\mathrm{MN}=\frac{1}{2}\mathrm{BC}$

$\Rightarrow 3=\frac{1}{2}\mathrm{BC}$

$\mathrm{BC}=6 \mathrm{~cm}$
Similarly,

$\mathrm{NP}=\frac{1}{2} \mathrm{AB}$

$\Rightarrow \mathrm{AB}=2 \times \mathrm{NP}$

$=2 \times 3.5$

$=7 \mathrm{~cm}$

$\mathrm{MP}=\frac{1}{2} \mathrm{AC}$

$\Rightarrow \mathrm{AC}=2 \times \mathrm{MP}$

$=2 \times 2.5$

$=5 \mathrm{~cm}$

Hence, $\mathrm{BC}=6 \mathrm{~cm}, \mathrm{AB}=7 \mathrm{~cm}$ and $\mathrm{AC}=5 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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