If the ratio of the corresponding sides of two similar triangles is 2 : 3, then find the ratio of their corresponding attitudes.

Answer

To solve the problem, we need to find the ratio of the corresponding altitudes of two similar triangles given the ratio of their corresponding sides.

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given that the ratio of the corresponding sides of two similar triangles is 2:3. Let's denote the two triangles as \( \triangle ABC \) and \( \triangle DEF \).

**Hint**: Identify the triangles and the ratio of their sides clearly.

2. **Set Up the Ratios**:
Since the triangles are similar, the ratio of any two corresponding sides is equal. Therefore, we can write:
\[ \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} = \frac{2}{3} \]

**Hint**: Remember that in similar triangles, all corresponding sides have the same ratio.

3. **Understanding Altitudes**:
The altitudes of the triangles from corresponding vertices are also proportional to the sides. Let \( h_1 \) be the altitude from vertex \( A \) to side \( BC \) in triangle \( ABC \), and \( h_2 \) be the altitude from vertex \( D \) to side \( EF \) in triangle \( DEF \).

**Hint**: Recognize that altitudes correspond to sides in similar triangles.

4. **Set Up the Ratio of Altitudes**:
Since the triangles are similar, we can say:
\[ \frac{h_1}{h_2} = \frac{AB}{DE} \]
Substituting the known ratio of the sides:
\[ \frac{h_1}{h_2} = \frac{2}{3} \]

**Hint**: The ratio of altitudes is equal to the ratio of corresponding sides.

5. **Conclusion**:
Therefore, the ratio of the corresponding altitudes of the two similar triangles is also \( 2:3 \).

**Final Answer**: The ratio of the corresponding altitudes is \( \frac{2}{3} \).