The bisector of an equilateral triangle is 11√3. Find its side.

Since the triangle is equilateral, the bisector drawn from its corner will also be the height and median. That is, since this is the height, a rectangular rectangle is formed, and since this is the median, it divides the side in half. Let’s take the whole side as 2x and half as x. Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs) 4x ^ 2 = x ^ 2 + (11 is the root of 3) ^ 2. 3x ^ 2 = 121 * 3, so x ^ 2 = 121, and x = 11. Since the side is 2x, we multiply 11 by 2 and get 22.
Answer: the side of the triangle is 22