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

$AC=6\sqrt{3}$

$CD=3\sqrt{3}$

$AD=a$

now, we can use Pythagoras theorem

and we get

$AC^2=CD^2+AD^2$

now, we can plug values

$(6\sqrt{3} )^2=(3\sqrt{3} )^2+a^2$

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