To determine the scale factor between the two triangles in the image, we compare corresponding sides of the two triangles.

The first triangle has side lengths:

• 6, 5, and 4.

The second triangle has side lengths:

• 9, 7.5, and 6.

To find the scale factor, we take the ratio of any pair of corresponding sides from the two triangles.

Let's compare the side lengths:

1. $\text{Scale factor for side } 6$ and $9$ is $\frac{9}{6} = 1.5$.
2. $\text{Scale factor for side } 7.5$ and $5$ is $\frac{7.5}{5} = 1.5$.
3. $\text{Scale factor for side } 6$ and $4$ is $\frac{6}{4} = 1.5$.

Since the scale factor is consistent for all corresponding sides, the scale factor between the two triangles is 1.5.

Would you like further details or have any other questions?

Here are five related questions to expand on this topic:

1. How do you find the scale factor if the triangles were oriented differently?
2. What does a scale factor less than 1 indicate about the size of the second triangle compared to the first?
3. Can you determine the area ratio of two similar triangles using the scale factor?
4. What happens to the perimeter of a triangle when you apply a scale factor?
5. How do you verify if two triangles are similar?

Tip: When working with scale factors, ensure you consistently compare corresponding sides to avoid errors in calculation.