Question

In the adjoining figure $XY||BC$.
$AX=p-3$, $BX=2p-2$ and $\frac{AY}{CY}=\frac{1}{4}$. Find '$p$'.

Answer 1

Given: In $△ABC,$ XY || BC $\therefore \frac{AX}{XB}=\frac{AY}{YC}$ ($\because$ Thales theorem)
$\frac{p-3}{2p-2}=\frac{1}{4}$
$\Rightarrow 4(p-3)=1(2p-2)$

$\Rightarrow 4p-12=2p-2$

$\Rightarrow 2p=10$ $\therefore p=5$