Q25 of 95 Page 5

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


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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