Question

In $\angle ABC$, $E$ is a point on $AB$, $F$ and $D$ are two points on $BC$ such that $EF$ parallel to $AD$ and $ED$ parallel to $AC$. If $BF=4$ cm, $FD=6$ cm, $BE=8$ cm, then $BC=$ ____

Answer 1

Let $AE=x$ and $DC=y$

In $△ABD$, we have

$EF\parallel AD,$

$\Rightarrow \frac{8}{x}=\frac{4}{6}$ ....(By Basic Proportionality Theorem)

$\Rightarrow x=12$

In $△ABC,$

$EF\parallel AC,$

$\Rightarrow \frac{8}{x}=\frac{10}{y}$

$\Rightarrow y=15$

Therefore, $BC=BD+DC=10$ cm $+15$ cm $=25$ cm