Question

$\ln a\Delta ABC,P$ and $Q$ are points on sides $AB$ and $AC$ respectively, such that PQ $\parallel BC$ . If $AP=3.6cm,AQ=6cm,QC=9cm$ and $BC=30cm,$ find $AB$ and $PQ$

Answer 1

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

By $AAA$ criteria

$\Delta ABC\sim \Delta APQ$

$⟹\frac{AB}{AP}=\frac{AC}{AQ}=\frac{BC}{PQ}\frac{AB}{3.6}=\frac{15}{6}=\frac{30}{PQ}⟹AB=18cm,BC=12cm$