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The image you uploaded contains a question about similar triangles. Let's analyze and solve it.

### Problem:
The problem involves two right-angled triangles, and you are asked to determine whether these triangles are similar, and if they are, to find the missing length.

### Given:
- One triangle has sides 10 (adjacent to the right angle) and 24 (hypotenuse).
- The other triangle has a side labeled \( x \) (adjacent to the right angle) and 15 (hypotenuse).

### Solution:

1. **Check for Similarity**:
   Triangles are similar if their corresponding angles are equal or if the ratios of their corresponding sides are proportional.

   Since both triangles are right-angled, they automatically have one angle equal (90°). To check if they are similar, compare the ratio of the sides.

2. **Set Up the Proportions**:
   \[
   \frac{10}{x} = \frac{24}{15}
   \]

3. **Solve for \( x \)**:
   Cross-multiply to solve for \( x \):
   \[
   10 \times 15 = 24 \times x
   \]
   \[
   150 = 24x
   \]
   \[
   x = \frac{150}{24} = 6.25
   \]

### Conclusion:
The triangles are similar, and the length of the side \( x \) is 6.25 units.

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Here are five questions related to this problem:
1. What are the conditions necessary for triangles to be similar?
2. How do you calculate the hypotenuse of a right-angled triangle if the other two sides are known?
3. Can you explain why the triangles in the problem are similar?
4. What other methods can be used to determine if triangles are similar?
5. How would the solution change if the triangles were not right-angled?

**Tip**: In problems involving similar triangles, always check the ratios of corresponding sides to confirm similarity before proceeding to find unknowns.

The sides marked on the right-angled triangles in the image are as follows: 10, x, and 24 for the first triangle, and 9, 15, and x for the second triangle. You are asked to determine if these triangles are similar and to find the length of the missing side x.

This problem involves determining the similarity of two right-angled triangles and finding the missing side length using the ratio of corresponding sides. Ideal for students in Grades 8-10, this exercise applies concepts of triangle similarity and proportionality.

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