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Which of the following expressions represents the perimeter of the figure below?

The perimeter \( P \) of a rectangle is calculated by adding up the lengths of all its sides. For a rectangle, the formula is:

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

In the image, the length of the rectangle is given as \( 3x - 2 \), and the width is \( 2x - 8 \).

So, the expression for the perimeter is:

\[
P = 2 \times \left( (3x - 2) + (2x - 8) \right)
\]

Now, simplify the expression inside the parentheses:

\[
(3x - 2) + (2x - 8) = 3x + 2x - 2 - 8 = 5x - 10
\]

Substitute this back into the formula for the perimeter:

\[
P = 2 \times (5x - 10) = 10x - 20
\]

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

\[
P = 10x - 20
\]

Would you like more details or have any questions? Here are 5 related questions to consider:
1. How do we find the perimeter of more complex polygons?
2. Can you express the perimeter as a function of \( x \)?
3. What is the perimeter if \( x = 5 \)?
4. How does the perimeter change as \( x \) increases?
5. How would you solve for \( x \) if the perimeter were given?

**Tip:** When working with expressions in geometry, always remember to group like terms to simplify calculations.

This problem involves calculating the perimeter of a rectangle where the length and width are given as algebraic expressions. Using the formula for the perimeter of a rectangle P = 2(Length + Width), this problem tests algebraic skills and geometry concepts, suitable for students in Grades 7-9.

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