Question

Find the altitude of an equilateral triangle whose side is a unit.
class-9th ​

Answer 1

The altitude of the euilateral triangle, bisects the base. 

Consider an equilateral triangle ABC, with AD as an altitude on BC

Hence,CD=a/2

In triangle ACD

AC^2=CD^2+AD^2(Pythagoras theorem

a^2=(a/2)^2+AD^2

AD^2=a^2-a^2/4

AD^2=3a^3/4

AD=root 3a/2