Answer :

Δ ABC is an equilateral triangle


By Pythagoras theorem in triangle ABD


AB2 = AD2 + BD2


but BD = 1/2 BC ( In a triangle, the perpendicular from the vertex to the base bisects the base)


thus AB2 = AD2 + {1/2 BC}2


AB2 = AD2 + 1/4 BC2


4 AB2 = 4AD2 + BC2


4 AB2 - BC2 = 4 AD2


(as AB = BC we can subtract them )


Thus 3AB2 = 4AD2

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