Find the length of the altitude of an equilateral triangle of side 2a cm.

Question

Philoid · Accepted Answer

Given: Side of equilateral triangle = 2a cm

To find: Length of altitude

Let ∆ ABC be an equilateral triangle with side 2a cm.

Let AD be the altitude of ∆ ABC.

Here, BD = DC = a

In ∆ ABD,

Using Pythagoras theorem, we have

AB² = AD² + BD²⇒ AD² = AB² – BD²⇒ AD² = (2a)² – (a)² = 4a² – a² = 3a²

⇒ AD² = 3a²

⇒ AD = √3a² = √3 a cm