To find the perimeter of a rectangle, the formula is:

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

Given:

• Width = $9v - 5w$
• Length = $9v + 6w$

Substitute these values into the formula for perimeter:

$\text{Perimeter} = 2 \times \left( (9v + 6w) + (9v - 5w) \right)$

Now, combine like terms inside the parentheses:

$(9v + 6w) + (9v - 5w) = 9v + 9v + 6w - 5w = 18v + w$

Thus, the perimeter is:

$\text{Perimeter} = 2 \times (18v + w) = 36v + 2w$

So, the expression for the perimeter is $36v + 2w$ centimeters.

Would you like any further details or clarifications?

Here are some related questions for practice:

1. How would the perimeter change if the width were doubled?
2. What is the perimeter if $v = 2$ and $w = 3$?
3. How do you find the area of a rectangle with the same width and length?
4. What happens to the perimeter if $w$ is increased by 5 cm?
5. Can you simplify the expression for perimeter if both $v$ and $w$ are 1?

Tip: Always double-check for any like terms before performing operations in algebraic expressions!