Question

A equilateral triangle has area of 9√3 find the length

Answer 1

as we know that area of equilateral triangle =√3a^2/4
9√3=√3a^2/4
or 9=a^2/4. (√3 to √3 has cancelled)
or a^2=36
a=√36
a=6.
thus the side of triangle will be 6.
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Answer 2

hi friend
here's your answer looking for

area of equilateral triangle =
$\\ \frac{ \sqrt{3} }{4} {a}^{2}$
so, if area is 9√3

then,

$9 \sqrt{3} = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ 36 \sqrt{3} = \sqrt{3 } {a}^{2} \\ \\ \frac{36 \sqrt{3} }{ \sqrt{3} } = {a}^{2} \\ \\ \sqrt{36} = a \\ \\ a = 6unit$
so this is your answer

hope you are satisfied with my answer