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Area of an Equilateral Triangle

Prove that in...

Question

Prove that in an equilateral triangle, three times the square of a side is equal to four times the square of its altitudes.

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Solution

Let ABC be an equilateral triangle and let.

In and we have

And

Since is a right triangle right-angled at D. So

Hence proved.

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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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