Final answer:
To find the dimensions of the rectangle, we used the given perimeter and the relationship between its length and width. By setting the width as x, we established the length as 5x and solved the equation derived from the perimeter formula, 108 = 2(5x + x), to find that x = 9 cm, making the length 45 cm.
Step-by-step explanation:
The question involves finding the dimensions of a rectangle given the perimeter and a relationship between its length and width. Let's denote the width of the rectangle by x. We are given that the length of the rectangle is five times the width, so the length will be 5x.
The formula for the perimeter (P) of a rectangle is P = 2(length + width), which in this case is P = 2(5x + x). We are given that the perimeter is 108 cm. Setting up the equation, we have:
108 = 2(5x + x)
108 = 2(6x)
108 = 12x
Dividing both sides by 12 gives us x = 9. Therefore, the width of the rectangle is 9 cm and the length is 5 times the width, which is 45 cm.
So, the dimensions of the rectangle are 45 cm by 9 cm.