Final answer:
The width of the rectangle is 13 inches and the length of the rectangle is 45 inches.
Step-by-step explanation:
To solve this problem, we can use the given information to set up an equation. Let's let the width be represented by 'w' and the length be represented by 'l'.
Given: The length of the rectangle is nine less than four times the width.
Translating this into an equation, we have: l = 4w - 9.
The problem also states that the perimeter of the rectangle is 92 inches. The formula for the perimeter of a rectangle is: P = 2(l + w).
Substituting the value of l from the first equation, we have: 92 = 2((4w - 9) + w).
Now, we can solve for w by simplifying the equation and isolating the variable. Once we find the value of w, we can substitute it back into the first equation to find the value of l.
The width of the rectangle is 13 inches and the length of the rectangle is 45 inches.