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The image shows two triangles that appear to be similar, with corresponding side lengths labeled. To find the unknown side length \( x \) in the larger triangle, we can use the properties of similar triangles.

### Step-by-Step Solution:

1. **Identify Corresponding Sides**: Since the triangles are similar, the ratios of their corresponding side lengths should be equal.

   - In the smaller triangle, we have sides of lengths \( 9.3 \), \( 10.2 \), and \( 11.2 \).
   - In the larger triangle, we have corresponding sides \( 18.6 \), \( 20.4 \), and \( x \) (unknown side).

2. **Set Up Proportion**: Let's use the corresponding sides \( 11.2 \) (small triangle) and \( x \) (large triangle). We can also use \( 10.2 \) (small triangle) and \( 20.4 \) (large triangle) as a pair for the proportion.

   \[
   \frac{11.2}{x} = \frac{10.2}{20.4}
   \]

3. **Solve the Proportion**: Cross-multiply to find \( x \).

   \[
   11.2 \cdot 20.4 = 10.2 \cdot x
   \]

   \[
   228.48 = 10.2 \cdot x
   \]

   \[
   x = \frac{228.48}{10.2}
   \]

   \[
   x \approx 22.4
   \]

### Answer:
The length of \( x \) is approximately \( 22.4 \).

Would you like more details or have any questions?

Here are five additional questions you might explore:
1. What are other ways to confirm that two triangles are similar?
2. How can we use the Pythagorean theorem with side lengths to verify similarity?
3. What is the scale factor between these two triangles?
4. How would we find the area ratio between the two triangles?
5. What other properties are preserved in similar triangles?

**Tip:** In similar triangles, corresponding side lengths are proportional, and angles are congruent, which makes them a powerful tool for solving geometry problems.

Find the unknown side length (x) in a pair of similar triangles based on their corresponding side lengths.

Learn how to solve for the unknown side length (x) in a pair of similar triangles by using proportionality between corresponding sides. The triangles have given side lengths of 9.3, 10.2, and 11.2 for the smaller triangle, and 18.6, 20.4, and x for the larger triangle. This problem is suitable for students in Grades 8-10 and demonstrates the properties of similar triangles.

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