Question

In the following figure drawn, line $PY$ $\parallel$ side $BC$, $AP=6$, $PB=12$, $AY=5$, $YC=x$, then find $x$.

Answer 1

In $\Delta ABC$, line $l$ $\parallel$ side $BC$,
By the Theorem of Basic Proportionality,
$\frac{AY}{YC}=\frac{AP}{PB}$
$\Rightarrow \frac{5}{x}=\frac{6}{12}$
$\Rightarrow x\times 6=5\times 12$
$\Rightarrow x=\frac{5\times 12}{6}$
$\Rightarrow x=5\times 2$
Therefore, $x=10$ units.