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 `PQ|| BC`.

In ΔAPQ and ΔABC,

\[\angle APQ = \angle B \] (Corresponding angles)

So,

\[∆ APQ~ ∆ ABC\] (AA Similarity)

\[\frac{AP}{AB} = \frac{PQ}{BC}\]

Substituting value AP = 3cm,AB=10cm and  PQ = 3cm, we get

`(AP)/(AB)=(3)/(BC)`

By cross multiplication we get

`4 xx BC = 3xx10`

`BC = (3xx10)/4`

`BC = 30/4`

`BC = 7.5 cm`

Hence, the value of BC is  7.5 cm.