In an equilateral triangle ABC, AE is an altitude on side BC. Show that three times square of one side of this triangle is equal to four times the square of its altitude AE.
Let side of equilateral triangle be a. And AE be the altitude of ABC
So, BE = EC = =
By applying Pythagoras theorem in ABE, we have:
AB2 = AE2 + BE2
4AE2 = 3a2.
Or, 4AE2 = 3 x (square of one side)2
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