Final answer:
The length of a side of the equilateral triangle is determined by evaluating the given expressions for x, y, and z, and substituting them into the perimeter formula. After calculation, the side length is found to be 16 cm.
Step-by-step explanation:
To determine the length of a side of an equilateral triangle with a given perimeter, we first need to express the perimeter in terms of x, y, and z, and then substitute the values of y and z in terms of x before solving. Given the perimeter (P) of the equilateral triangle is (x² + y + 5z) cm, and we know that x= -2, y= -2x, and z= 2y, we substitute the values to find y and z: y = -2(-2) = 4 and z = 2(4) = 8.
Now, substituting y and z back into the perimeter equation gives us P = (-2)² + 4 + 5(8) = 4 + 4 + 40 = 48 cm. Since the triangle is equilateral, all sides are equal, so we divide the perimeter by 3 to find the length of one side: Side length = P/3 = 48/3 = 16 cm. Therefore, the length of a side of the equilateral triangle is 16 cm.