In an equilateral triangle, prove that three times the square of one side is equal to fourtimes the square of one of its altitudes
Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC
BE = EC =
= 
Applying Pythagoras theorem in ΔABE, we obtain
AB2 = AE2 + BE2
a2 = AE2 + 
2
AE2 = a2 – 
AE2 = 
4AE2 = 3a2
4 × (Square of altitude) = 3 × (Square of one side)
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