In a ∆ ABC, D and E are points on AC and BC respectively,

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In a ∆ ABC, D and E are points on AC and BC respectively, AB and DE are perpendicular to BC. If AB = 9 cm , DE = 3 cm and AC = 24 cm, then AD is :

1. 32cm
2. 16cm
3. 8 cm
4. 4 cm

Correct Option: B

According to question , we draw a figure triangle ABC

In ∆ ABC and ∆ DEC
AB || DE
Given that , AB = 9 cm , DE = 3 cm and AC = 24 cm
∴ ∠ABC = ∠DEC = 90°
∠CAB = ∠CDE
By AA-similarity theorem,
∆ ABC ~ ∆DEC

∴	AB	=	AC
	DE		CD

⇒	9	=	24
	3		CD

⇒ 3 =	24
	CD

⇒ CD =	24	= 8 cm.
	3

∴ AD = AC – CD = 24 – 8 = 16 cm