Question

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

Answer 1

In triangle ABC, P and Q are points on sides AB and AC respectively such that.

In ΔAPQ and ΔABC,

$\angle APQ=\angle B\left(\mathrm{Corresponding}\mathrm{angles}\right)$

$\angle PAQ=\angle BAC\left(\mathrm{Common}\right)$

So, $∆\mathrm{APQ}~∆\mathrm{ABC}$ (AA Similarity)

$\frac{AP}{AB}=\frac{PQ}{BC}$

Substituting value and , we get

By cross multiplication we get

Hence, the value of BC is .