Let's solve this step by step.

Given that the length and width of a rectangle are consecutive integers, we can represent them as $x$ (the smaller integer) and $x + 1$ (the larger integer).

The formula for the perimeter of a rectangle is:

$P = 2 \times (\text{length} + \text{width})$

Substituting the given perimeter and the expressions for the length and width:

$38 = 2 \times (x + (x + 1))$

Simplify the equation:

$38 = 2 \times (2x + 1)$

$38 = 4x + 2$

Now, subtract 2 from both sides:

$36 = 4x$

Divide both sides by 4:

$x = 9$

So, the width is $x = 9$ feet, and the length is $x + 1 = 10$ feet.

Final Answer:

• Width: 9 feet
• Length: 10 feet

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. If the perimeter of a rectangle is 48 feet and the length is twice the width, what are the dimensions?
2. What are the dimensions of a rectangle with an area of 50 square feet if the length is 1 foot longer than the width?
3. A rectangle has a perimeter of 60 feet. If the length is 5 feet more than twice the width, what are the dimensions?
4. The length of a rectangle is 3 feet more than the width, and its area is 154 square feet. What are the dimensions of the rectangle?
5. If the perimeter of a square is equal to the perimeter of a rectangle with a width of 8 feet and a length of 10 feet, what is the side length of the square?

Tip: For consecutive integer problems, always consider the relationship between the variables to simplify the equation.