# In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its alitudes.

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In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

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Given :- An equilateral triangle with one of its altitude.

Let a be the side of the equilateral triangle.

∴ BE = EC = BC/2 = a/2

To prove :- 4AE2 = 3a2

In △ABE, by pythagoras theorem

Hence proved that three times the square of one side is equal to four times the square of one of its altitudes.