⊥A of ∆ ABC is a right angle. AD is perpendicular

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⊥A of ∆ ABC is a right angle. AD is perpendicular on BC. If BC = 14 cm and BD = 5 cm, then measure of AD is :

1. 2√5cm.
2. √5 cm.
3. 3√5 cm.
4. 3.5√5 cm.

Correct Option: C

In ∆ ABC and ∆ DAC,
∠ADC = ∠BAC , ∠C = ∠C
By AA – similarity criterion,
∆ ABC ~ ∆ DAC

∴	AB	=	BC	=	AC
	DA		AC		DC

⇒	CB	=	AC
	CA		CD

⇒ CA² = CB × CD
= BC (BC – BD)
= 14 × (14 – 5) = 14 × 9
= 126 sq. cm.
∴ From ∆ ADC
CA² = AD² + C’D²
⇒ 126 = AD² + 9²
⇒ AD² = 126 – 81 = 45
⇒ AD = √45 = 3√5cm.