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Write an expression to represent the perimeter of each figure. Simplify the expression then evaluate it when n = 4.

 



To find the expression for the perimeter of the given quadrilateral, we need to add up the lengths of all the sides. The lengths of the sides are given as:

- \( 2n - 5 \)
- \( 3n - 4 \)
- \( n + 3 \)
- \( 2n + 1 \)

### Step 1: Write the perimeter expression
The perimeter \( P \) is the sum of all sides:

\[
P = (2n - 5) + (3n - 4) + (n + 3) + (2n + 1)
\]

### Step 2: Simplify the expression
Now, combine like terms:

\[
P = (2n + 3n + n + 2n) + (-5 - 4 + 3 + 1)
\]

\[
P = 8n - 5
\]

### Step 3: Evaluate when \( n = 4 \)
Substitute \( n = 4 \) into the simplified expression:

\[
P = 8(4) - 5 = 32 - 5 = 27
\]

Thus, the perimeter of the figure when \( n = 4 \) is 27 units.

Would you like more details on the steps, or do you have any questions?

Here are 5 related questions you could explore:
1. How would the perimeter change if one of the side expressions was doubled?
2. Can you find the perimeter if \( n = 5 \)?
3. What is the perimeter of a square with side length \( 3n - 4 \)?
4. How do different values of \( n \) affect the shape of this quadrilateral?
5. Can you solve for the area of this quadrilateral with the given side lengths?

**Tip:** Always simplify algebraic expressions step by step, combining like terms carefully to avoid errors.

Write an expression to represent the perimeter of each figure. Simplify the expression then evaluate it when n = 4.

Learn how to find the perimeter of a quadrilateral with side lengths represented by algebraic expressions. The problem involves simplifying expressions and evaluating the perimeter when n = 4. Suitable for students in Grades 7-9.

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