The width of a rectangle measures left parenthesis, 9, v, minus, 5, w, right parenthesis(9v−5w) centimeters, and its length measures left parenthesis, 9, v, plus, 6, w, right parenthesis(9v+6w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

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!

The width of a rectangle measures (9v − 5w) centimeters, and its length measures (9v + 6w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Learn how to find the perimeter of a rectangle using algebraic expressions. Given the width (9v − 5w) cm and length (9v + 6w) cm, discover the step-by-step solution to calculate the perimeter, resulting in the expression 36v + 2w cm. This problem is suitable for students in Grades 8-10.

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