The width of a rectangle measures left parenthesis, 5, v, minus, 2, w, right parenthesis(5v−2w) centimeters, and its length measures left parenthesis, 6, v, plus, 7, w, right parenthesis(6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

The formula for the perimeter \( P \) of a rectangle is given by:

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

Here, the width \( W \) of the rectangle is \( (5v - 2w) \) cm, and the length \( L \) is \( (6v + 7w) \) cm. Plugging these expressions into the perimeter formula:

\[
P = 2 \times \left[(6v + 7w) + (5v - 2w)\right]
\]

### Step-by-step Solution

1. **Add the length and the width:**

\[
(6v + 7w) + (5v - 2w) = 6v + 5v + 7w - 2w
\]

2. **Combine like terms:**

\[
6v + 5v = 11v \quad \text{and} \quad 7w - 2w = 5w
\]

So, the sum of the length and width is:

\[
11v + 5w
\]

3. **Multiply by 2 to find the perimeter:**

\[
P = 2 \times (11v + 5w) = 22v + 10w
\]

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

\[
22v + 10w \text{ centimeters}
\]

Would you like a detailed explanation of any part of this solution, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would the expression for the perimeter change if the width was \( (7v - 3w) \) and the length was \( (4v + 5w) \)?
2. How would you express the area of the rectangle in terms of \( v \) and \( w \)?
3. What is the perimeter if \( v = 3 \) cm and \( w = 2 \) cm?
4. If the perimeter of the rectangle is given, how can you find the values of \( v \) and \( w \)?
5. How does changing the values of \( v \) and \( w \) affect the perimeter?

**Tip:** Always combine like terms before performing arithmetic operations when simplifying algebraic expressions.

The width of a rectangle measures (5v−2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Learn how to calculate the perimeter of a rectangle with variable dimensions. This problem involves algebraic expressions for length and width, and demonstrates the application of the perimeter formula. Suitable for Grades 7-9 students looking to strengthen their geometry and algebra skills.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation