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ABC is an equilateral triangle with AD perpendicular to BC , prove that AD² = 3DC².

Posted by Srusti Samikshya 5 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 3 months ago

Here given triangle ABC must be an equilateral triangle and we have to prove AD² = 3DC²

Solution:

Given: ∆ABC is an equilateral, AD ⊥ BC.

In right ∆ABD,

AB² = BD² + AD²

⇒ BC² = BD² + AD² (AB = BC)

⇒ (2BD)² = BD² + AD² [From (1)]

⇒ 4BD² = BD² + AD²

⇒ AD² = 3BD² = 3DC² [As BD = DC]

Hence proved

0Thank You

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