The width of a rectangle measures left parenthesis, 8, u, minus, 4, right parenthesis(8u−4) centimeters, and its length measures left parenthesis, 8, u, minus, 2, right parenthesis(8u−2) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

To find the perimeter of a rectangle, you can use the formula:

\[
P = 2 \times (\text{length} + \text{width})
\]

Given the width \( (8u - 4) \) cm and the length \( (8u - 2) \) cm, we can substitute these expressions into the formula.

First, add the length and the width:

\[
\text{length} + \text{width} = (8u - 2) + (8u - 4)
\]

Combine like terms:

\[
(8u - 2) + (8u - 4) = 8u + 8u - 2 - 4 = 16u - 6
\]

Now, multiply this sum by 2 to find the perimeter:

\[
P = 2 \times (16u - 6)
\]

Distribute the 2:

\[
P = 2 \times 16u - 2 \times 6 = 32u - 12
\]

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

\[
\boxed{32u - 12 \text{ cm}}
\]

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

Here are 5 related questions to expand your understanding:
1. How do you find the area of a rectangle given its length and width?
2. What happens to the perimeter of a rectangle if both the length and the width are doubled?
3. How do you express the perimeter of a square in terms of the side length?
4. If \( u = 1 \), what is the perimeter of this rectangle?
5. How would you find the length and width if the perimeter and one dimension were given?

**Tip:** When combining like terms, make sure to align similar variables to simplify the expression accurately.

The width of a rectangle measures (8u - 4) centimeters, and its length measures (8u - 2) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Learn how to calculate the perimeter of a rectangle with algebraic expressions for length and width. This example uses the formula P = 2 × (length + width) and demonstrates how to combine like terms for an expression like (8u - 4) and (8u - 2). Suitable for Grades 6-8 students learning geometry and algebra.

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