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 use the formula:

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

Given that:
- Width \( = 8u - 4 \) cm
- Length \( = 8u - 2 \) cm

Substitute the given expressions into the perimeter formula:

\[
P = 2 \times \left( (8u - 4) + (8u - 2) \right)
\]

Simplify inside the parentheses:

\[
P = 2 \times \left( 8u - 4 + 8u - 2 \right)
\]
\[
P = 2 \times (16u - 6)
\]

Now, distribute the 2:

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

Thus, the expression representing the perimeter of the rectangle is:

\[
P = 32u - 12 \, \text{cm}
\]

Would you like a detailed explanation of any step? 

Here are 5 related questions you can explore:
1. How do you calculate the area of the same rectangle?
2. How does changing the value of \( u \) affect the perimeter?
3. What is the perimeter when \( u = 3 \)?
4. How does the formula for the perimeter differ from the formula for the area of a rectangle?
5. What are some applications of perimeter calculations in real life?

**Tip**: When simplifying algebraic expressions, always combine like terms before applying distributive properties to make calculations easier.

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 where the width is (8u−4) cm and the length is (8u−2) cm. This problem involves algebraic concepts such as the distributive property and combining like terms. Ideal for students in Grades 6-8.

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