The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 38 feet. Find the length and width of the rectangle.

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.

Learn how to find the dimensions of a rectangle with consecutive integer length and width, given its perimeter. This problem involves using the formula for the perimeter of a rectangle and solving a linear equation. Suitable for students in Grades 6-8.

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