∆ ABC is a triangle, PQ is line segment intersecting

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∆ ABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is

1. 28 cm.
2. 48 cm.
3. 84 cm.
4. 42 cm.

Correct Option: B

On the basis of question we draw a figure of triangle ABC in which PQ is line segment intersecting AB in P and AC in Q ,

Here , AP : BP = 3 : 5 and PQ = 18 cm
PQ || BC
∴ ∠APQ = ∠ABC
∠AQP = ∠ACB
By AA – similarity theorem,
∆APQ ~ ∆ABC

∴	AB	=	BC
	AP		PQ

⇒	AB - AP	=	BC - PQ
	AP		PQ

⇒	BP	=	BC - PQ
	AP		PQ

⇒	5	=	BC - 18
	3		18

⇒ BC - 18 =	5	× 18 = 30
	3

⇒ BC = 30 + 18 = 48 cm.