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

Question

Philoid · Accepted Answer

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