Question

In a $\Delta ABC$, P and Q are points on sides AB and AC respectively, such that PQ || BC. If 2.4 cm, AQ =2 cm, QC = 3cm and BC =6cm, Finnd AB and PQ.

Answer 1

$\Delta APQ$~$\Delta ABC$ because it is given that $PQ\parallel BC$
$\frac{AP}{PB}=\frac{AQ}{QC}$
$\frac{AP}{PB}=\frac{AQ}{AC}=\frac{PQ}{BC}$
$AC=AQ+QC$
$\Rightarrow 2+3=5cm$
hence,
$\frac{2.4}{AB}=\frac{2}{5}$
$\Rightarrow AB=6$
$\frac{2}{5}=\frac{PQ}{BC}$
$\Rightarrow PQ=\frac{2}{5}$ x BC
$\Rightarrow \frac{12}{5}=2.4cm$