To determine the scale factor between two similar triangles, we compare corresponding sides.

In the image you provided:

• The left triangle has a side of length 16.
• The right triangle has a corresponding side of length 13.

The scale factor is the ratio of the side length of the right triangle to the corresponding side length of the left triangle. So, we calculate:

$\text{Scale Factor} = \frac{13}{16}$

This fraction is already in its simplest form, so the scale factor is 13/16.

Do you need further clarification or additional details on this? Here are some follow-up questions:

1. How can you check if two triangles are similar besides comparing sides?
2. If the scale factor were 1, what would that imply about the two triangles?
3. How would you find the area of a triangle if given its base and height?
4. What happens to the area of a triangle if you scale its sides by a factor of $k$?
5. How would you calculate the perimeter of a triangle given the lengths of all sides?

Tip: When dealing with similar shapes, always make sure to compare corresponding sides or angles correctly.