The ratio between the altitudes of two similar triangles is 3 : 5, write the ratio between their :
perimeters.

Answer

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

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that the ratio of the altitudes of two similar triangles is given as 3:5. Let's denote the two triangles as Triangle ABC and Triangle PQR.

2. **Setting Up the Ratios**:
Since the triangles are similar, the ratio of their corresponding sides is equal to the ratio of their altitudes. Therefore, we can write:
\[ \frac{AM}{PN} = \frac{3}{5} \]
where AM is the altitude of Triangle ABC and PN is the altitude of Triangle PQR.

3. **Using the Property of Similar Triangles**:
For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. Hence, we can express the ratio of the perimeters as:
\[ \frac{\text{Perimeter of } \triangle ABC}{\text{Perimeter of } \triangle PQR} = \frac{AB}{PQ} = \frac{3}{5} \]

4. **Conclusion**:
Therefore, the ratio of the perimeters of the two triangles is also 3:5.

### Final Answer:
The ratio between the perimeters of the two similar triangles is **3 : 5**.

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