Question

In a ΔABC, 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.

Answer 1

We have || BC

Therefore, by BPT

We have,

`"AP"/"PB"="AQ"/"QC"`

`2.4/"PB"=2/3`

`rArr"PB"=(3xx2.4)/2=(3xx24)/2=(3xx6)/5=18/5`

⇒ PB = 3.6 cm

Now, AB = AP + PB

= 2.4 + 3.6 = 6cm

Now, In ΔAPQ and ΔABC

∠A = ∠A [common]

∠APQ = ∠ABC [∵ PQ || BC ⇒ Corresponding angles are equal]

⇒ ΔAPQ ~ ΔABC [By AA criteria]

`rArr"AB"/"AP"="BC"/"PQ"`        [corresponding sides of similar triangles are proportional]

`rArr"PQ"=(6xx2.4)/6`

⇒ PQ = 2.4 cm

Hence, AB = 6 cm and PO = 2.4 cm