https://file.aiquickdraw.com/mathbot/file/1730062801922lw6e4keg.jpg

In part (b) of the image, it appears to show a right triangle with side lengths and potentially a square or rectangular shape inside, where each side is labeled with "x." However, the exact text or problem description is unclear, so I'll give a general solution approach for finding "x" based on typical geometric relationships in such problems.

To solve for \( x \), let's consider these common steps depending on the arrangement:

### Step-by-Step Solution Approach:
1. **Identify the Larger Triangle Dimensions**:
   - The triangle’s dimensions may include a hypotenuse and two legs, often noted with a specific measurement or relation.
   
2. **Establish Relations for the Inner Shape**:
   - If the inner shape is a square with side \( x \), each side of the square should be equal.
   - Set up equations based on the right triangle’s properties, such as the Pythagorean theorem or similarity.

3. **Use Similar Triangles** (if applicable):
   - If the inner shape creates smaller triangles within the larger triangle, these may be similar. 
   - This similarity can provide proportional relationships between the sides of these triangles and the side \( x \).

4. **Apply the Pythagorean Theorem**:
   - For a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \), use \( a^2 + b^2 = c^2 \) to solve for any unknown lengths.
   
5. **Solve for \( x \)**:
   - After establishing equations, isolate \( x \) and solve.

If you could confirm the exact text or measurements, I can provide a more precise solution.

Would you like to go over any specific method or need further explanation on a step?

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**Related Questions**:
1. How do you find the area of a triangle with a square inside?
2. What are the properties of similar triangles?
3. How is the Pythagorean theorem used in solving for unknowns in triangles?
4. What strategies are useful for solving problems with inscribed squares?
5. How do geometric shapes within shapes influence their proportional relationships?

**Tip**: In right triangles, identifying similar triangles can simplify many problems by allowing you to set up proportional relationships between sides.

Learn how to solve for x in a right triangle containing an inscribed square, with a step-by-step approach using the Pythagorean theorem and triangle similarity principles. Suitable for students in Grades 8-10.

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