Question

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

Answer 1

Let AD be the altitude in the given equilateral triangle, ΔABC.

We know that altitude bisects the opposite side.

∴ BD = DC = a

In ΔADB

∠ADB = 90º

Applying pythagoras theorem we obtain

AD² + DB² = AD²

⇒ AD² + a² = (2a)²

⇒ AD² + a² = 4a²

⇒ AD² = 3a²

⇒ AD =`asqrt3`

In an equilateral triangle, all the altitudes are equal in length. Therefore, the length of each altitude will be `sqrt3a`