Given:
We need to find the length of the rectangle.
Steps to find the length of the rectangle:
1. Express the length in terms of the width:
l = w + 7
2. Use the formula for the area of a rectangle:
Area = l × w
Substitute the given area and the expression for l :
60 = (w + 7) × w
3. Form a quadratic equation:
60 = w² + 7w
Rewrite in standard form:
w² + 7w − 60 = 0
4. Factorize the left side of the equation:
w² + 12w − 5w − 60 = 0
w (w + 12) −5(w + 12) = 0
(w + 12)(w − 5) = 0
5. Possible values of w :
w = 5
w = −12 (not possible because width cannot be negative)
6. Determine the length using the width found:
l = w + 7 = 5 + 7 = 12
Therefore, the length of the rectangle is:
[tex]\boxed{12\text{ feet}}[/tex]