The area of an equilateral triangle is 9√3 cm ^ 2, and its perimeter is 18 cm. Find the height of the triangle.

First, let’s find the length of the side of this equilateral triangle.
Let us denote it by a.
In the initial data for this task, it is reported that the sum of the lengths of all sides of this triangle is 18 cm, therefore, we can draw up the following equation:
a + a + a = 18,
solving which, we get:
3a = 18;
a = 18/3 = 6 cm.
According to the condition of the problem, the area of ​​this triangle is 9√3 cm ^ 2.
Applying the formula for the area of ​​a triangle in terms of the length of the side and the height drawn to this side, we find the height h of this equilateral triangle:
h = 2 * 9√3 / 6 = 18√3 / 6 = 3√3 cm.
Answer: 3√3 cm.