**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 :- 4AE^{2} = 3a^{2}

**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.**