ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Let AD be the altitude of the given equilateral triangle, ΔABC

We know that altitude bisects the opposite side

BD = DC = a

In triangle ADB,

∠ADB = 90^O

Using Pythagoras theorem, we get

AD² + DB² = AB²

AD² + a² = (2a)²

AD² + a² = 4a²

AD² = 3a²

AD = a

In an equilateral triangle, all the altitudes are equal in length.

Hence, the length of each altitude will be