Question

Find the height of an equilateral triangle of side 12 cm.

Answer 1

Let ABC be the equilateral triangle with AD as an altitude from A meeting BC at D. Then, D will be the midpoint of BC.
Applying Pythagoras theorem in right-angled triangle ABD, we get:  

 

`AB^2=AD^2+BD^2` 

`⇒ AD^2=12^2-6^2(∵BD=1/2 BC=6)` 

`⇒AD^2=144-36=108` 

`⇒AD=sqrt108=6sqrt3 cm` 

Hence, the height of the given triangle is `6sqrt3` cm.