In aΔ ABC, P and Q are points on sides AB and AC respectively, such that PQ||BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ.

Given: AP = 2.4 cm

AQ = 2 cm

QC = 3 cm

BCC = 6 cm

To find: The length of AB and PQ

Theorem Used:

Basic proportionality theorem:

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides into same ratio.

Explanation:

As PQ∥BC

By basic proportionality theorem,

We have,

PB = 3 x 1.2

PB = 3.6 cm

Now AB = AP + PB

AB = 2.4 + 3.6

AB = 6 cm

Now IN ∆ APQ and ∆ ABC

∠A=∠A [Common]

∠APQ=∠ABC [PQ∥BC]

∆ APQ ~∆ ABC [By AA criteria]

⇒ PQ=2.4 cm