Final answer:
The length of the rectangle is found by setting up a quadratic equation using the area 90 square feet and the relationship that the width is one foot shorter than the length. The length turns out to be 10 feet.
Step-by-step explanation:
To find the length of the rectangle given that the area is 90 square feet and the width is 1 foot shorter than the length, we can set up an equation. Let length be L and width be W. The width is one foot shorter than the length, so W = L - 1. The area of a rectangle is Length × Width, that is L × W, so:
L × (L - 1) = 90
L^2 - L - 90 = 0
Solving this quadratic equation, we find that the positive solution is L = 10 feet. Therefore, the length of the rectangle is 10 feet.