Answer: An equilateral triangle has three equal sides and three equal angles of 60 degrees each. Let's denote the length of one side of the equilateral triangle as "s" and the length of the altitude as "h."
We know that the perimeter of the triangle is 240 cm, which means that:
3s = 240
Dividing both sides by 3, we get:
s = 80
Now, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3)/4) x s^2
Plugging in the values of s, we get:
Area = (sqrt(3)/4) x 80^2 = 1388.22 cm^2
We also know that the area of an equilateral triangle can be expressed as:
Area = (1/2) x s x h
Plugging in the values of s and solving for h, we get:
1388.22 = (1/2) x 80 x h
h = 1388.22 / 40 = 34.71 cm
Therefore, the length of the altitude of the equilateral triangle is x√3 = 34.71 cm. Solving for x, we get:
x = 34.71 / sqrt(3) ≈ 20