The side of an equilateral triangle is 18√3 cm. Find the bisector of this triangle.

In an equilateral triangle, the bisector is both the median dividing the opposite side in half and the height making a right angle with the side on which it is lowered. Therefore, we can find its length according to the Pythagorean theorem as the unknown leg of a right-angled triangle, in which the hypotenuse is equal to the side of this triangle 18√3 cm, and the known leg is half of the side 9√3 cm.

√ (18√3) ^ 2 – (9√3) ^ 2 = √ (324 * 3 – 81 * 3) = √243 * 3 = √729 = 27 cm.

Answer: the bisector is 27 cm.