https://file.aiquickdraw.com/mathbot/file/1725467666280p1nbevpb.jpg

The image shows two similar triangles, and you are asked to find the ratio of the lengths of the corresponding sides.

### Step-by-Step Solution:

1. **Identify the corresponding sides of the triangles:**
   - Small Triangle: \( 5 \, \text{m} \) and \( 6 \, \text{m} \).
   - Large Triangle: \( 20 \, \text{m} \) and \( 24 \, \text{m} \).

2. **Find the ratio of the corresponding sides:**
   - Corresponding sides:
     - \( 5 \, \text{m} \) corresponds to \( 20 \, \text{m} \).
     - \( 6 \, \text{m} \) corresponds to \( 24 \, \text{m} \).

3. **Calculate the ratios:**
   - Ratio of the first pair of sides: 
     \[
     \frac{5}{20} = \frac{1}{4}
     \]
   - Ratio of the second pair of sides:
     \[
     \frac{6}{24} = \frac{1}{4}
     \]

4. **Conclusion:**
   - The ratio of the lengths of the corresponding sides of the similar triangles is \( \frac{1}{4} \).

Would you like more details or have any other questions?

### Follow-Up Questions:
1. How do you determine if two triangles are similar?
2. What properties do similar triangles share?
3. How can you use ratios to find missing side lengths in similar triangles?
4. What is the significance of the similarity ratio in real-world applications?
5. How does the ratio of side lengths relate to the ratio of perimeters in similar figures?

**Tip:** In similar triangles, the corresponding angles are equal, and the corresponding sides are proportional.

Find the ratio of the lengths of corresponding sides for the similar triangles.

Learn how to find the ratio of the lengths of corresponding sides for similar triangles using geometry concepts and the similarity theorem. This example involves calculating the ratios of side lengths and understanding proportional relationships between similar triangles. Suitable for students in Grades 6-8.

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