In •ABC, D and E are the points of sides AB and BC respectively

Home » Aptitude » Mensuration » Question

In •ABC, D and E are the points of sides AB and BC respectively such that DE || AC and AD : DB = 3 : 2. The ratio of area of trapezium ACED to that of ∆ BED is

DE ∥ AC ∴ ∆ DBE ≅ ∆ ABC

∆ AD	=	EC	=	3
DB	=	EB	=	2

AD	+ 1 =	3	+ 1
DB		2

⇒	AB	=	5
	DB		2

∴	∆ ABC	=	AB²	=	25
	∆ DBE		BD²		4

⇒	∆ ABC	- 1 =	25	- 1
	∆ DBE		4

⇒	∆ ABC - ∆ DBE	=	25 - 4
	∆ DBE		4

⇒	∎ ACED	=	21	or 21 : 4
	∆ DBE		4