To solve this problem, we need to find the value of $x$ given that the perimeter of the rectangle is 44 feet.

Step-by-Step Solution:

1. Identify the dimensions of the rectangle: The length of the rectangle is $17 - 2x$ and the width is $x + 7$.

2. Use the formula for the perimeter of a rectangle: The perimeter $P$ of a rectangle is given by:

   $P = 2 \times (\text{Length} + \text{Width})$

   Plugging in the values:

   $44 = 2 \times \left( (17 - 2x) + (x + 7) \right)$

3. Simplify the equation:

   Combine like terms inside the parentheses:

   $44 = 2 \times (17 - 2x + x + 7)$

   $44 = 2 \times (24 - x)$

   Now, divide both sides by 2:

   $22 = 24 - x$

4. Solve for $x$:

   $x = 24 - 22$

   $x = 2$

Conclusion:

The value of $x$ is 2 feet.

Would you like more details, or do you have any questions?

Relative Questions:

1. How do you find the area of this rectangle using the given dimensions?
2. What happens if the perimeter changes to a different value?
3. How would the solution change if the length and width were switched?
4. What are some practical applications of perimeter in real life?
5. Can we find the diagonal length of this rectangle using the Pythagorean theorem?

Tip:

When solving for unknowns, always check your solution by substituting back into the original equation to verify that it satisfies all given conditions.