Final answer:
The dimensions of the rectangle are a width of 12cm and a length of 28cm.
Step-by-step explanation:
To find the dimensions of the rectangle, we can set up an equation using the given information. Let's let the width be x. Since the length is 8cm less than three times the width, the length is 3x - 8. The equation to represent the perimeter is 2(length + width) = 64. Plugging in the values, we get 2(3x - 8 + x) = 64. Simplifying and solving for x, we find that x = 12. Therefore, the width of the rectangle is 12cm and the length is 3(12) - 8 = 28cm.