Question

In $△$ ABC, P and Q are points on sides AB and AC respectively such that PQ $\parallel$ BC. If AP = 4 cm, PB = 6 cm and PQ = 3 cm, determine BC.

Answer 1

In $△ABC$, $PQ\parallel BC$

So, by proportionality theorem

$\frac{AP}{PB}=\frac{AQ}{QC}=\frac{PQ}{BC}$

$\frac{4}{6}=\frac{AQ}{QC}=\frac{3}{BC}$

$\Rightarrow$ $\frac{4}{6}=\frac{3}{BC}$

$\therefore$ $BC=4.5cm$