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.