# prove that "three times of any side of an equilateral triangle is equal to four times the squares of the altitude?"

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then altitude = x√3 / 2

4 times altitude = 4 × (x√3 / 2)^2

= 4 × (3x^2 / 4)

= 3x^2

= 3 times the square of side.

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See diagram.

Use Pythagoras theorem in the right angle triangle ADC.

AC² = AD² + DC²

a² = h² + (BC/2)² a² = h² + a² / 4

* h² = a² - a²/4 = 3a²/4*

* 4 h² = 3 a²*

Use Pythagoras theorem in the right angle triangle ADC.

AC² = AD² + DC²

a² = h² + (BC/2)² a² = h² + a² / 4