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Let's analyze the given problem.

You have an L-shaped figure with some known side lengths: 
- The bottom left part has dimensions 5 ft and 14 ft.
- The vertical part is 8 ft and 10 ft, and we need to find the missing side, labeled as "?". 

Since the sides of this shape meet at right angles, we can use the principle of subtracting the total lengths to find the missing side.

1. The total length of the left vertical side is \( 15 \, \text{ft} \), and it is made up of two parts: the given 5 ft and the unknown side. Therefore, the missing side is \( 15 - 5 = 10 \, \text{ft} \).

Thus, the missing side length is **10 ft**.

Would you like more detailed steps, or do you have any questions about this?

Here are 5 related questions to explore further:
1. How can we apply the Pythagorean theorem to solve for unknown sides in right-angled shapes?
2. What if there were more complex L-shaped figures with multiple unknowns?
3. How does the Pythagorean theorem apply to non-right-angled triangles?
4. How would you solve for missing sides in shapes with diagonal measurements?
5. What are the properties of various common 2D shapes like rectangles, squares, and parallelograms?

Tip: Always break down complex shapes into smaller, manageable parts to solve for unknowns step-by-step!

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

Learn how to find the missing side length in an L-shaped figure where all intersecting sides meet at right angles. This geometry problem covers key concepts such as subtracting lengths and understanding geometric properties in right-angled shapes. Suitable for students in Grades 5-7.

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