The bisector of an equilateral triangle is 9√3. Find its side

In an equilateral triangle, all angles are 60 degrees
The bisector divides the angle in half, we get
Two right triangles
180 – 60 – 30 = 90 degrees
The bisector in an equilateral triangle is the height
One leg of the bisector equals 9√3
Hypotenuse – 2x
The second leg against an angle of 30 degrees is equal to half of the hypotenuse – x
We compose the equation according to the Pythagorean theorem
x * x + 81 * 3 = 4x * x
4x * x – x * x = 243
3x * x = 243
x * x = 243/3 = 81
x = 9
Answer = 9