Let ABC be the equilateral triangle whose side is 2a cm.
Let us draw altitude AD such that AD ⊥ BC.
We know that altitude bisects the opposite side.
So, BD = DC = a cm.
In ADC, ∠ADC = 90°.
We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, by applying Pythagoras Theorem,
AC2 = AD2 + DC2
(2a cm)2 = AD2 + (a cm)2
4a2 cm2 = AD2 + a2 cm2
AD2 = 3a2 cm2
AD = √3 a cm
The length of altitude is √3 a cm.
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