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In a 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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by safty

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by safty

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Let ABC be equilateral triangle.

Let AD be perpendicular bisector from A on to BC. So BD = CD = 1/2 BC

ADC is a right angle triangle. So AC² = AD² + DC²

AC² = AD² + (1/2 AC)²

AD² = 3/4 AC²

4 AD² = 3 AC²

Let AD be perpendicular bisector from A on to BC. So BD = CD = 1/2 BC

ADC is a right angle triangle. So AC² = AD² + DC²

AC² = AD² + (1/2 AC)²

AD² = 3/4 AC²

4 AD² = 3 AC²