The width of a rectangle measures left parenthesis, 10, u, plus, 3, right parenthesis(10u+3) centimeters, and its length measures left parenthesis, 7, u, minus, 8, right parenthesis(7u−8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

The perimeter \( P \) of a rectangle is calculated using the formula:

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

Given:
- Width \( = 10u + 3 \) cm
- Length \( = 7u - 8 \) cm

Substitute these expressions into the perimeter formula:

\[
P = 2 \times \left( (10u + 3) + (7u - 8) \right)
\]

Now simplify the expression inside the parentheses:

\[
P = 2 \times \left( 10u + 7u + 3 - 8 \right)
\]
\[
P = 2 \times \left( 17u - 5 \right)
\]

Finally, distribute the 2:

\[
P = 2 \times 17u - 2 \times 5
\]
\[
P = 34u - 10
\]

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

\[
P = 34u - 10 \, \text{cm}
\]

Would you like a detailed breakdown or have any questions?

### 5 Related Questions:
1. How do you calculate the area of a rectangle with given expressions for length and width?
2. What happens to the perimeter if \( u \) increases or decreases?
3. How does changing the length or width affect the perimeter of the rectangle?
4. Can you express the perimeter formula for any general rectangle with variable length and width?
5. How does this perimeter compare to the area for the same rectangle?

### Tip:
Always remember to simplify expressions inside parentheses before applying further operations like multiplication.

The width of a rectangle measures (10u+3) centimeters, and its length measures (7u−8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Learn how to calculate the perimeter of a rectangle with given expressions for the length (7u-8) and width (10u+3). This step-by-step solution demonstrates key algebraic and geometric concepts, suitable for students in Grades 6-8.

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