Question

In the given figure, line $PY\parallel$ side $BC$, $AP=4$, $PB=8$, $AY=5$ and $YC=x$. Find $x$.

Answer 1

In $\Delta ABC$, line $PY\parallel$ side $BC$.
By the theorem of B.P.T.,
Thus $\frac{AY}{YC}=\frac{AP}{PB}$
$\Rightarrow \frac{5}{x}=\frac{4}{8}$
$\Rightarrow x\times 4=5\times 8$
$\Rightarrow x=\frac{5\times 8}{4}$
$\Rightarrow x=5\times 2$
Therefore, $x=10$ units