In an equilateral △ABC,AD ⊥BC, prove that \(AD^2=38D^2\), – InterviewSolution

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1.

In an equilateral △ABC,AD ⊥BC, prove that \(AD^2=38D^2\),

Answer»

We have

⊿ ABC is an equilateral triangle and AD⊥BC

In ⊿ ADB⊿ ADC

∠ADB = ∠ADC = 90° AB = AC (Given)

AD = AD (Common)

⊿ ADB ≅⊿ ADC (By RHS condition)

∴ BD = CD = BC/2 ……. (i)

In ⊿ ABD

BC²= AD²+ BD²

BC² = AD²+ BD² [Given AB = BC]

(2BD)²= AD² + BD² [From (i)]

4BD²- BD² = AD²

AD² = 3BD²

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