If ABC is a equilateral triangle AD perpendicular AB. Find ADsquare =3

1.	If ABC is a equilateral triangle AD perpendicular AB. Find ADsquare =3BD square
Answer» According to the question,\xa0{tex}\\triangle ABC {/tex}\xa0is an equilateral triangle.In {tex}\\triangle{/tex}ABD, using Pythagoras theorem,{tex}\\Rightarrow{/tex} AB2 = AD2 + BD2{tex}\\Rightarrow{/tex} BC2 = AD2 + BD2, (as AB = BC = CA){tex}\\Rightarrow{/tex} (2 BD)2 = AD2 + BD2, (perpendicular is the median in an equilateral triangle){tex}\\Rightarrow{/tex} 4BD2 - BD2 = AD2{tex}\\therefore{/tex}\xa03BD2 = AD2

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