If in ∆ ABC, DE||BC, AB = 7.5 cm, BD = 6 cm. and DE

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If in ∆ ABC, DE||BC, AB = 7.5 cm, BD = 6 cm. and DE = 2cm, then the length of BC in cm is :

1. 6
2. 8
3. 10
4. 10.5

Correct Option: C

According to question , we draw a figure

Here , AB = 7.5 cm, BD = 6 cm. and DE = 2cm
In ∆ ADE and ∆ ABC,
∵ DE | | BC
∵ ∠D = ∠B ; ∠E = ∠C
∴ By AA - similarity,
∆ ADE ~ ∆ ABC

∴	AD	=	DE
	AB		BC

⇒	AB - BD	=	DE
	AB		BC

⇒	7.5 - 6	=	2
	7.5		BC

⇒	1.5	=	2
	7.5		BC

⇒	1	=	2	⇒ BC = 2 × 5 = 10 cm.
	5		BC