Question

ΔABC is am equilateral triangle of side 2a units. Find each of its altitudes.  

 

Answer 1

 

Let AD, BE and CF be the altitudes of ΔABC meeting BC, AC and AB at D, E and F, respectively.
Then, D, E and F are the midpoint of BC, AC and AB, respectively.
In right-angled ΔABD, we have:   

AB = 2a and BD = a
Applying Pythagoras theorem, we get: 

`AB^2=AD^2+BD^2` 

`AD^2=AB^2-BD^2=(2a)^2-a^2` 

`AD^2=4a^2-a^2=3a^2` 

`AD=sqrt3a  units`

 Similarly, 

`BE=asqrt3  unit and CF=a sqrt3  unitst`