In ∆ ABC, ∠A = 90°, AD ⊥ BC and AD = BD

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In ∆ ABC, ∠A = 90°, AD ⊥ BC and AD = BD = 2 cm. The length of CD is

1. 3 cm
2. 3.5 cm
3. 3.2 cm
4. 2 cm

Correct Option: D

According to question , we draw a figure ∆ ABC

Given , ∠A = 90°, AD ⊥ BC and AD = BD = 2 cm.
In ∆ ABD,
∴ AB = √AD² + BD²
AB = √2² + 2²
AB = √8
AB = 2√2 cm.
∆ ABD ~ ∆BCA

∴	AB	=	BD
	BC		AB

⇒ AB² = BC × BD
⇒ (2√2)² = BC × 2
⇒ 8 = BC × 2

⇒ BC =	8	= 4 cm.
	2

∴ CD = BC – BD = (4 – 2) cm = 2 cm.