In a ∆ ABC, D and E are two points on AB and AC respectively

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In a ∆ ABC, D and E are two points on AB and AC respectively such that DE || BC, DE bisects the ∆ ABC in two equal areas. Then the ratio DB : AB is

1. 1 : √2
2. 1 : 2
3. ( √2 – 1) : √2
4. √2 : 1

Correct Option: C

According to question , we draw a figure of triangle ABC in which D and E are two points on AB and AC respectively such that DE || BC ,

Given , ∆ ADE = ☐ BDEC
⇒ ∆ 2ADE = ∆ ABC
DE || BC
∴ ∆ ADE ~ ∆ ABC

∴	∆ ADE	=	1	=	AD²
	∆ ABC		2		AB²

⇒	AB	= √2
	AD

⇒	AB	- 1 = √2 - 1
	AD

⇒	AB - AD	= √2 - 1
	AD

⇒	BD	= √2 - 1
	AD

∴	BD	=	BD	×	AD	=	√2 - 1
	AB		AD		AB		√2