Question

In an equilateral triangle abc, ADis perpendicular yo BC, then find
AD2

Answer 1

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]

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Answer 2

Let the sides of equilateral triangle be x cm.
Acq,
AD is altitude.
Formula of altitude of equi. triangle is root under 3 / 2 side .
side = x cm.
therefore altitude = root 3 /2 x cm. (AD(
AD^2 = 3/4 x^2