Question

In an equilateral ΔABC,AD⊥BC, prove that AD² = 3BD².

Answer 1

Answer:

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Answer 2

Here is your answer

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

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]