2. The ratio of the perimeters of two similar triangles is 3/5. The scale factor is ________

1. Break Down the Problem

To find the scale factor of two similar triangles based on the ratio of their perimeters, we need to understand the relationship between the perimeters and the sides of similar triangles.

2. Relevant Concepts

For similar triangles:

• The ratio of the perimeters is equal to the ratio of the corresponding sides.
• If the ratio of the perimeters of two similar triangles is given by $\frac{A}{B}$, then the scale factor $k$ can be expressed as:

$k = \frac{A}{B}$

3. Analysis and Detail

Given the ratio of the perimeters of the two triangles is $\frac{3}{5}$:

• Let $A = 3$ and $B = 5$.
• The scale factor $k$ will then be:

$k = \frac{3}{5}$

4. Verify and Summarize

The calculation confirms that the scale factor is derived directly from the ratio of perimeters. Thus, we can conclude that the scale factor between the two triangles is:

Final Answer

The scale factor is $\frac{3}{5}$.