https://file.aiquickdraw.com/mathbot/file/17261197342057f6doiek.jpg

The image presents a pentagon with side lengths labeled as follows:  
- \( 2y \)  
- \( 11 \)  
- \( y + 3 \)  
- \( 3y - 3 \)  
- \( 11 \)  

The problem states that the perimeter of the pentagon is 64 units, and we are tasked with finding the value of \( y \).

### Step-by-step solution:

The perimeter of a polygon is the sum of the lengths of its sides. In this case, the sides of the pentagon are given by:

\[
\text{Perimeter} = 2y + 11 + (y + 3) + (3y - 3) + 11
\]

Simplify the expression:

\[
\text{Perimeter} = 2y + 11 + y + 3 + 3y - 3 + 11
\]

Combine like terms:

\[
\text{Perimeter} = (2y + y + 3y) + (11 + 3 - 3 + 11)
\]

\[
\text{Perimeter} = 6y + 22
\]

We are told the perimeter is 64 units, so:

\[
6y + 22 = 64
\]

Solve for \( y \):

\[
6y = 64 - 22
\]

\[
6y = 42
\]

\[
y = \frac{42}{6}
\]

\[
y = 7
\]

Thus, the value of \( y \) is \( 7 \).

### Final Answer:
\[
y = 7
\]

Would you like further details on any step?  

Here are 5 related questions for practice:
1. What is the perimeter of a hexagon with side lengths depending on variables like \( y \)?
2. How would you solve a similar problem for a hexagon instead of a pentagon?
3. Can you find the side lengths after solving for \( y \)?
4. How would you approach this problem if one of the side lengths was missing?
5. What would the value of \( y \) be if the perimeter were different?

**Tip**: When working with polygon problems, always combine like terms carefully to avoid mistakes in variable expressions!

The perimeter of the pentagon below is 64 units. Find the value of y.

Solve for the value of y in a pentagon where the perimeter is 64 units. This problem uses algebra and geometric principles such as combining like terms and the formula for the perimeter of polygons. Suitable for students in Grades 7-9.

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