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 ΔABC such that AD = 8 cm, BD = 12 cm, AE = 6 cm and EC = 9 cm. Then find BC/ DE.

Since	AD	=	AE	=	2
	DB		EC		3

∴ DE || BC (by converse of BPT)
∴ ΔADE ∼ ΔABC (AA similarity)

AD	=	DE
AB	=	BC

8	=	DE
AB	=	BC

2	=	DE	⇒	BC	=	5
5	=	BC	⇒	DE	=	2