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To determine the scale factor between the two triangles, we compare the corresponding sides of the smaller triangle to the larger triangle. The triangles appear to be similar since their corresponding angles and sides are proportional. Let's calculate the scale factor by comparing the sides:

1. The smaller triangle has sides of lengths 6, 8, and 10.
2. The larger triangle has sides of lengths 12, 16, and 20.

We can use the ratio of any pair of corresponding sides to find the scale factor. Let's use the smallest side for simplicity:

\[
\text{Scale Factor} = \frac{\text{larger triangle side}}{\text{smaller triangle side}} = \frac{12}{6} = 2
\]

Thus, the scale factor is **2**.

### Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What are the properties of similar triangles?
2. How do you calculate the area ratio between two similar triangles?
3. If the area of the smaller triangle is given, how can we find the area of the larger triangle?
4. How does the scale factor relate to the perimeters of the triangles?
5. Can the scale factor be found using non-corresponding sides?

**Tip:** The ratio of the areas of two similar figures is the square of the scale factor.

Learn how to determine the scale factor between two similar triangles using their corresponding sides. This problem involves applying the similarity criteria for triangles and calculating ratios. Suitable for students in Grades 9-12 studying geometry.

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