Question

In figure, E and F are mid - points of the sides AB and AC respectively of the $\Delta ABC$. G and H are mid-points of the sides AE and AF respectively of the $\Delta AEF$. If GH =1.8 cm, find BC.

Answer 1

$EF=\frac{1}{2}BC\dots \dots \left(1\right)$
($\because$ E and F are mid-points of sides AB and AC of $\Delta ABC$)
$GH=\frac{1}{2}EF\dots \dots \left(2\right)$
($\because$ G and H are mid-points of sides AB and AC of $\Delta AEF$)
From (1) and (2), we have,
$GH=\frac{1}{2}\times \frac{1}{2}BC=\frac{1}{4}BC$
$\Rightarrow BC=4\times GH=4\times 1.8cm=7.2cm$
Hence, BC = 7.2 cm