The ratio of corresponding sides of two similar triangles is `2:3`, then the ratio of the perimeters of two triangles is `4:9` (True/False).

Answer

To determine whether the statement "The ratio of the perimeters of two triangles is 4:9" is true or false, given that the ratio of corresponding sides of two similar triangles is 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Similar Triangles**:
- We know that if two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters.

2. **Given Ratio of Sides**:
- The ratio of the corresponding sides of the two similar triangles is given as \( \frac{2}{3} \).

3. **Finding the Ratio of Perimeters**:
- Since the triangles are similar, the ratio of their perimeters will be the same as the ratio of their corresponding sides. Therefore, the ratio of the perimeters will also be \( \frac{2}{3} \).

4. **Comparing with Given Statement**:
- The statement claims that the ratio of the perimeters is \( \frac{4}{9} \).
- We have found that the actual ratio of the perimeters is \( \frac{2}{3} \), which is not equal to \( \frac{4}{9} \).

5. **Conclusion**:
- Since \( \frac{2}{3} \) is not equal to \( \frac{4}{9} \), the statement is **False**.

### Final Answer:
The statement is **False**.

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