Question

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

Answer 1

We know that the altitude of an equilateral triangle bisects the side on which it stands and forms right-angled triangles with the remaining sides.

Suppose ABC is an equilateral triangle having AB = BC = CA = 2a.

Suppose AD is the altitude drawn from the vertex A to the side BC.

So, it will bisects the side BC.

∴ DC = a

Now, In right triangle ADC.

By using Pythagoras theorem, we have

AC² = CD² + DA² 

⇒ (2a)² = a² + DA²  

⇒ DA² = 4a² – a² 

⇒ DA² = 3a² 

⇒ `DA = sqrt(3)a` 

Hence, the length of the altitude of an equilateral triangle of side 2a cm is `sqrt(3)`a cm.