D and E are the points on the sides AB and AC respectively

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D and E are the points on the sides AB and AC respectively of a ∆ ABC and AD = 8 cm, DB = 12 cm, AE = 6 cm and EC = 9 cm, then BC is equal to :

1. 2 DE
  5
2. 5 DE
  2
3. 3 DE
  2
4. 2 DE
  3

Correct Option: B

As per the given in question , we draw a figure triangle ABC whose D and E are the points on the sides AB and AC respectively

Here , AD = 8 cm, DB = 12 cm, AE = 6 cm and EC = 9 cm
According to the question,

	AD	=	8	=	2
	DB		12		3

	AE	=	6	=	2
	EC		9		3

∴	AD	=	AE	=	2
	DB		EC		3

⇒	DB	=	EC	=	3
	AD		AE		2

⇒	DB + AD	=	3 + 2	=	EC + AE
	AD		2		AE

⇒	AB	=	5	=	AC
	AD		2		AE

∴ ∆ ABC ~ ∆ ADE

∴	AB	=	BC	=	5
	AD		DE		2

⇒ BC =	5	DE
	2