In an equilateral triangle, prove that three times the square on one side is equal to four times the square of it's altitude
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Let a is the length of the side of equilateral triangle and AE is the altitude.
So BE = EC = BC/2 = a/2
Now in triangle ABC,
From Pythagoras Theorem
AB2 = AE2 + BE2
=> a2 = AE2 + (a/2)2
=> AE2 = a2 - a2 /4
=> AE2 = 3a2 /4
=> 4AE2 = 3a2
=> 4*(square of altitude) = 3*(square of one side)
So three times the square of one side is equal to four times the square of one of its altitudes.
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