Question

What is the length of the altitude of the equilateral triangle below?

Answer 1

we are given

equilateral triangle

we can see that triangle ACD is a right angled triangle

so, we can use Pythagoras theorem for this triangle

hypotenuse=AC

Adjacent=CD

opposite=AD=a

and

`AC=6√(3)`

`CD=3√(3)`

`AD=a`

now, we can use Pythagoras theorem

and we get

`AC^2=CD^2+AD^2`

now, we can plug values

`(6√(3) )^2=(3√(3) )^2+a^2`

now, we can solve for a

`108=27+a^2`

`27+a^2-27=108-27`

`a^2=81`

`a=9`

so, option-A..........Answer