In a ∆ ABC, DE || BC. D and E lie on AB and AC respectively.

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In a ∆ ABC, DE || BC. D and E lie on AB and AC respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.

1. 2 : 3
2. 3 : 2
3. 3.5 : 2
4. 7 : 2

Correct Option: C

We draw a figure triangle ABC in which DE || BC. D and E lie on AB and AC respectively,

DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
∴ By AA - similarity theorem,
∆ ADE ~ ∆ ABC

	AB	=	BC
	AD		DE

⇒	AB	=	BC
	AB - BD		DE

⇒	7	=	BC
	7 - 3		DE

⇒	BC	=	7	=	3.5	= 3.5 : 2
	DE		4		2