In triangle ABC, DE || BC where D is a point on AB and

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In triangle ABC, DE || BC where D is a point on AB and E is a point on AC. DE divides the area of ∆ABC into two equal parts. Then DB : AB is equal to

DE || BC Area of ∆ADE = Area of quadrilateral BDEC
⇒ Area of ∆ABC = 2 × Area of ∆ADE
In ∆ADE and ∆ABC,
∠D = ∠B ; ∠E = ∠C
∴ ∆ADE ~ ∆ABC

∴	Area of ∆ABC	=	AB²
	Area of ∆ADE		AD²

⇒	AB²	= 2 ⇒ AB = √2AD
	AD²

⇒ AB = √2(AB – DB)
⇒ √2AB – AB = √2 DB
⇒ AB (√2 – 1) = √2DB

⇒	DB	=	√2 - 1
	AB		√2