8.In an equilateral triangle ,prove that three times the square of one side is equal to four times the square of one of its altitudes.
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To prove: 3AB² = 4AE²
Proof: Let each side of one equilateral ∆ = a
BE = 1/2a -[perpendicular bisects the side in on an equilateral ∆]
In right ∆AEB, by Pythagoras theorem
(AB)²=(AE)² + (BE)²
(a)² = (AE)² + (1/2a)²
a² = AE² + (a/2)²
a²– a²/4 = AE²
3a²/4 = AE²
3a² = 4AE²
3AB² = 4AE²
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