Q. 254.6( 12 Votes )

In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3AB2= 4AD2.

Answer :


Given: ABC is an equilateral triangle


and AD is the altitude on side BC


To Prove: 3AB2= 4AD2


In right triangle ∆ADB, using Pythagoras theorem


(Perpendicular)2 + (Base)2 = (Hypotenuse)2


AD2 + BD2 = AB2



4AD2 + BC2 = 4AB2


4AD2 = 4AB2 – BC2


4AD2 = 4AB2 – AB2 [ABC is an equilateral triangle]


4AD2 = 3AB2


Hence Proved


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