Final answer:
The width of the rectangle is 9 inches, and the length is 18 inches, determined by setting up an equation using the perimeter formula and solving for the width.
Step-by-step explanation:
The question asks us to find the length and the width of a rectangle given that the length is 9 inches more than the width and the perimeter is 54 inches. To solve this, let's denote the width of the rectangle as w inches. Hence, the length will be w + 9 inches.
The formula for the perimeter P of a rectangle is 2 times the sum of the length l and the width w, which is P = 2(l + w). Plug in the perimeter and the expressions for the length and width:
2(w + 9 + w) = 54
2(2w + 9) = 54
2w + 9 = 27
2w = 18
w = 9
Thus, the width of the rectangle is 9 inches. To find the length, we add 9 to the width:
Length = Width + 9
Length = 9 + 9
Length = 18
So the width of the rectangle is 9 inches and the length is 18 inches.