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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