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Question -

In an equilateral triangle, prove that threetimes the square of one side is equal to four times the square of one of itsaltitudes.



Answer -

Given, an equilateral triangle say ABC,

Let the sides of the equilateral triangle beof length a, and AE be the altitude of ΔABC.

∴ BE = EC = BC/2 = a/2

In ΔABE, by Pythagoras Theorem, we get

AB2 = AE2 + BE2

4AE2 = 3a2

⇒ 4 × (Square of altitude) = 3 × (Square of one side)

Hence, proved.

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