To solve the problem, we need to find the expression for the perimeter of the rectangle.

Given:

• Width $w = 8u - 2v$ centimeters
• Length $l = 5u + 9v$ centimeters

The formula for the perimeter $P$ of a rectangle is:

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

Substituting the given expressions for the length and width:

$P = 2 \times \left[(5u + 9v) + (8u - 2v)\right]$

First, simplify the expression inside the parentheses:

$P = 2 \times \left[(5u + 8u) + (9v - 2v)\right]$

$P = 2 \times \left[13u + 7v\right]$

Now, distribute the 2:

$P = 26u + 14v$

Thus, the expression that represents the perimeter of the rectangle in centimeters is:

$\boxed{26u + 14v}$

Would you like further details or have any questions?

Here are five related questions:

1. How do you derive the area of the rectangle given the same width and length expressions?
2. What would the perimeter be if $u = 1$ and $v = 2$?
3. How would the perimeter formula change if the length and width expressions were multiplied by a constant factor?
4. Can you explain why the distributive property was used in simplifying the perimeter expression?
5. What are other common formulas involving rectangles that can be derived using similar algebraic techniques?

Tip: Always remember to double-check your algebraic steps to ensure accuracy when combining like terms.