P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2 cm, PB = 4 cm, AQ = 3 cm and QC = 6 cm, show that BC = 3PQ.

Question

Philoid · Accepted Answer

There are two triangles here, ∆APQ and ∆ABC. We shall prove these triangles to be similar.

&

⇒

Also, ∠A = ∠A [common angle]

So by AA-similarity criteria,

∆APQ ∼ ∆ABC

Thus,

And we know

⇒ BC = 3×PQ

Hence, proved.