1. Set up the equations:

* Let 'l' represent the length of the rectangle.

* Let 'w' represent the width of the rectangle.

We know:

* Perimeter: 2l + 2w = 18

* Area: l * w = 14

2. Solve for one variable:

* From the perimeter equation, we can solve for 'l':

2l = 18 - 2w

l = 9 - w

3. Substitute into the area equation:

* Substitute the expression for 'l' into the area equation:

(9 - w) * w = 14

4. Solve the quadratic equation:

* Expand the equation: 9w - w² = 14

* Rearrange into standard quadratic form: w² - 9w + 14 = 0

* Factor the quadratic: (w - 7)(w - 2) = 0

* Solve for 'w': w = 7 or w = 2

5. Find the length:

* For w = 7: l = 9 - 7 = 2

* For w = 2: l = 9 - 2 = 7

Conclusion:

The rectangle could have the following dimensions:

* Length = 7 feet, Width = 2 feet

* Length = 2 feet, Width = 7 feet

Since a rectangle can be oriented in two ways, both of these solutions are valid.