Question

In a $\Delta ABC,P$ and $Q$ are points on sides $AB$ and $AC$ respectively, such that PQ $\parallel BC$ . If $AP=2.4cm,AQ=2cm,QC=3cm$ and $BC=10cm,$ find $AB$ and $PQ$

Answer 1

$PQ||BC\angle A=\angle A\angle P=\angle B\angle Q=\angle C$

By $AAA$ criteria

$\Delta ABC\sim \Delta APQ$

$⟹\frac{AB}{AP}=\frac{AC}{AQ}=\frac{BC}{PQ}$

$\frac{AB}{2.4}=\frac{5}{2}=\frac{10}{PQ}$

$⟹AB=6cm,PQ=4cm$