Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.
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Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC. ∴ BE = EC = BC/2 = a/2 Applying Pythagoras theorem in ΔABE, we get AB2 = AE2 + BE2 ⇒ 4 × (Square of altitude) = 3 × (Square of one side)Read more on Sarthaks.com - https://www.sarthaks.com/2420/equilateral-triangle-prove-that-three-times-square-side-equal-four-times-square-altitudes
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