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

This triangle is equilateral, which means that its bisector is also height.

Let the original triangle be ABC, its bisector (height) – BH = 9√3.

△ ABH – rectangular, AH = 0.5AC (by the property of the bisector in an equilateral triangle) = 0.5AB.

Let AH = x. Then AC = 2x.

By the Pythagorean theorem for △ ABH:

BH ^ 2 + AH ^ 2 = AB ^ 2.

(9√3) ^ 2 + x ^ 2 = (2x) ^ 2.

243 + x ^ 2 = 4x ^ 2.

243 = 3x ^ 2.

81 = x ^ 2.

x = 9 = AH.

AB = AC = BC = 2AH = 18.

Answer: 18.