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The problem in the image is asking to find the length of \( x \) in a right triangle. Given the dimensions, we can solve this using the Pythagorean theorem.

### Problem Recap:
- Triangle \( \triangle ABC \) is a right triangle.
- The length of side \( AB = 10.5 \).
- The length of side \( AC = x \).
- The length of side \( BC = 9 \).
- The length of side \( DE = 3.5 \).

### Approach:
To find \( x \), we can apply the Pythagorean theorem, which states:

\[
AB^2 = AC^2 + BC^2
\]

### Substituting the given values:

\[
10.5^2 = x^2 + 9^2
\]

### Solve for \( x \):

1. Calculate the squares of the given numbers:
   \[
   10.5^2 = 110.25
   \]
   \[
   9^2 = 81
   \]

2. Substitute these into the equation:
   \[
   110.25 = x^2 + 81
   \]

3. Solve for \( x^2 \):
   \[
   x^2 = 110.25 - 81
   \]
   \[
   x^2 = 29.25
   \]

4. Take the square root of both sides:
   \[
   x = \sqrt{29.25} \approx 5.41
   \]

So, the length of \( x \) is approximately \( 5.41 \) units.

---

Do you want further details or have any questions? Here are 5 related questions you might find helpful:

1. How does the Pythagorean theorem apply to different types of triangles?
2. Can you explain how to calculate the square root without a calculator?
3. What are the implications if the triangle isn't a right triangle?
4. How would the problem change if you were given the hypotenuse and one leg?
5. What are some real-world applications of the Pythagorean theorem?

**Tip:** Always double-check your work by verifying the calculation steps, especially when working with squared numbers and square roots.

Find the length of x in a right triangle, where AB = 10.5, BC = 9, and DE = 3.5.

Learn how to find the length of x in a right triangle where AB = 10.5, BC = 9, and DE = 3.5. This problem applies the Pythagorean theorem to solve for x, with a detailed step-by-step solution. Suitable for students in Grades 8-10.

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