https://file.aiquickdraw.com/mathbot/file/17286508768508ikwqskw.jpg

The problem shown in the image is asking to find the perimeter of a rectangle, with sides labeled by expressions involving the variable \( w \). The lengths of the sides are:

- Two of the sides are labeled \( 7w - 6 \)
- The other two sides are labeled \( 2w \)

### Perimeter of a Rectangle Formula:
The perimeter \( P \) of a rectangle is given by:

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

In this case, the lengths are \( 7w - 6 \) and the widths are \( 2w \). Applying this to the formula:

\[
P = 2 \times \left( (7w - 6) + 2w \right)
\]

### Simplification:
First, simplify the expression inside the parentheses:

\[
P = 2 \times (7w - 6 + 2w) = 2 \times (9w - 6)
\]

Now distribute the \( 2 \):

\[
P = 2 \times 9w - 2 \times 6 = 18w - 12
\]

### Final Answer:
The simplified expression for the perimeter is:

\[
P = 18w - 12
\]

Would you like more details or have any questions about this solution?

### Related Questions:
1. What is the perimeter of the rectangle if \( w = 2 \)?
2. How do you find the perimeter if the lengths were labeled \( 8w - 3 \) and the widths were \( w + 5 \)?
3. How does the perimeter change if the expressions for the sides were different, such as \( 5w + 4 \) and \( 3w - 2 \)?
4. Can you write a general formula for the perimeter if the length is \( aw + b \) and the width is \( cw + d \)?
5. What happens to the perimeter when \( w \) becomes a negative number?

### Tip:
Always remember to simplify the expression inside the parentheses before multiplying by 2 when calculating the perimeter of rectangles using algebraic expressions.

Find the perimeter of a rectangle with sides labeled as 7w - 6 and 2w. Simplify your answer.

Learn how to calculate the perimeter of a rectangle where the lengths are given by the polynomials 7w - 6 and 2w. This step-by-step guide simplifies the expression to find the correct perimeter, covering key algebraic concepts. Suitable for students in Grades 8-10.

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