Final answer:
The dimensions of the rectangle where the perimeter is 180 cm and the length is eight times the width are 80 cm by 10 cm.
Step-by-step explanation:
To find the dimensions of the rectangle where the length is eight times the width, and the perimeter is 180 cm, we will define the width as w and the length as 8w. Since the perimeter (P) of a rectangle is twice the sum of its length and width (P = 2l + 2w), we substitute the given values to set up the equation: 180 = 2(8w) + 2w. Simplifying gives us 180 = 16w + 2w, and further simplification leads to 18w = 180. Dividing both sides by 18, we find that w = 10 cm, which is the width of the rectangle. To find the length, we multiply the width by 8, giving us a length of 80 cm. Therefore, the dimensions of the rectangle are 80 cm by 10 cm.