In ∆ ABC, E and D are points on sides AB and AC respectively

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In ∆ ABC, E and D are points on sides AB and AC respectively such that ∠ABC = ∠ADE. If AE = 3 cm, AD = 2 cm and EB = 2 cm, then length of DC is

1. 4 cm
2. 4.5 cm
3. 5.0 cm
4. 5.5 cm

Correct Option: D

As per the given in question , we draw a figure triangle ABC

Here , AE = 3 cm, AD = 2 cm and EB = 2 cm,
In ∆ ADE and ∆ ABC,
∠ABC = ∠ADE
∠A = ∠A
∴ ∆ ABC ~ ∆ ADE

∴	AB	=	BC	=	AC
	AD		DE		AE

∴	AB + EB	=	AC
	AD		AE

⇒	3 + 2	=	AC
	2		3

⇒	5	=	AC
	2		3

⇒ 2AC = 5 × 3 ⇒ AC =	15
	2

⇒ DC = AC – AD

DC =	15	- 2 =	15 - 4	=	11
	2		2		2

DC = 5.5 cm