https://file.aiquickdraw.com/mathbot/file/1726185711178j7yzbh6w.jpg

To solve the questions provided in the image, let's address each part:

### Part (a): Simplified Expression for the Perimeter of the Rectangle

The perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]

From the image, the length of the rectangle is \( 2n - 3 \) and the width is \( 4 \).

Substituting these values, we get:
\[ P = 2((2n - 3) + 4) \]
\[ P = 2(2n - 3 + 4) \]
\[ P = 2(2n + 1) \]
\[ P = 4n + 2 \]

So, the simplified expression for the perimeter is \( 4n + 2 \).

### Part (b): Solve for \( n \) Given Perimeter is 26

We know from part (a) that the perimeter is \( 4n + 2 \). Given that this equals 26, we set up the equation:
\[ 4n + 2 = 26 \]

Solving for \( n \):
\[ 4n = 26 - 2 \]
\[ 4n = 24 \]
\[ n = \frac{24}{4} \]
\[ n = 6 \]

Hence, the value of \( n \) that satisfies the given perimeter is \( 6 \).

Would you like more details on any steps or have other questions on this topic? Here are some related questions:

1. How would you find the area of the rectangle with the same dimensions?
2. What if the width was a different algebraic expression, how would that change the perimeter calculation?
3. Can you solve for \( n \) if the perimeter was a different value, say 30?
4. How does the solution change if the length is given as \( 2n - 3 \) and width as \( n + 1 \)?
5. What are some real-life applications of using algebra to solve for perimeter and area in planning and architecture?

**Tip:** When solving algebraic equations, always check your solution by substituting back into the original equation to ensure it holds true.

a) Write a simplified expression for the perimeter of the rectangle. b) The perimeter of the rectangle is 26. Work out the value of n.

Learn how to simplify the perimeter expression for a rectangle with dimensions 2n - 3 and 4, and solve for n when the perimeter is given as 26. This problem explores algebraic expressions and geometric formulas, ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation