https://file.aiquickdraw.com/mathbot/file/1726793019872hohzfvse.jpg

The image shows a polygon with various side lengths provided, and we are tasked with finding the missing side. The shape is an L-shaped figure, composed of rectangles, and the sides given are labeled in feet. Let's break this down:

### Given Dimensions:
- Vertical side on the left = 9 ft
- Horizontal side on the top = 6 ft
- Vertical segment in the middle = 5 ft
- Horizontal bottom = 14 ft
- Horizontal middle = 8 ft

### Strategy:
The key here is to realize that the L-shape is composed of two rectangles, and the vertical and horizontal sides should balance out across the shape.

1. **Vertical sides**:
   - The total height of the figure is 9 ft (leftmost vertical side).
   - The other vertical parts are 5 ft and the unknown side (let's call it \( x \)).
   - Therefore:  
     \[
     9 \, \text{ft} = 5 \, \text{ft} + x
     \]
     Solving for \( x \):
     \[
     x = 9 \, \text{ft} - 5 \, \text{ft} = 4 \, \text{ft}
     \]

Thus, the missing vertical side is **4 ft**.

Would you like more details or have any questions about this process?

Here are five relative questions:
1. How would you calculate the perimeter of this L-shaped figure?
2. Can you find the area of the shape using these dimensions?
3. What is the difference between calculating perimeter and area for composite shapes like this?
4. How would the problem change if one of the sides was missing horizontally instead?
5. Can you find another method to confirm the length of the missing side?

**Tip**: When working with composite shapes, breaking them down into simpler geometric figures helps simplify calculations.

Find the missing side length. Assume that all intersecting sides meet at right angles.

This problem involves finding the missing side length of an L-shaped figure. Use algebraic relationships to balance vertical and horizontal sides, solving for the unknown dimension. Appropriate for students in Grades 6-8, this problem reinforces the understanding of composite shapes and right-angle properties.

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