Final answer:
By factoring the quadratic expression for the area of the rectangle, which is x² + 13x + 36, we find that the length is 5 feet longer than the width.
Step-by-step explanation:
The area of a rectangle is given by the equation x² + 13x + 36. To find out how much longer the length is than the width, we can factor this quadratic equation, assuming that the length (l) and width (w) are the factors of the area.
Factoring the quadratic expression, we get:
(x + 9)(x + 4) = x² + 13x + 36
This means one dimension of the rectangle is x + 9 and the other is x + 4. The difference between the length and the width is:
(x + 9) - (x + 4) = 5
So, the length is 5 feet longer than the width.