The problem involves two right triangles where the triangle on the right is a scaled copy of the triangle on the left. We are tasked with identifying the scale factor.

In the left triangle, the two side lengths are given as:

• One leg: 5
• The other leg: 12

In the right triangle, the corresponding side lengths are:

• One leg: 25/4
• The other leg: 15

To find the scale factor, we compare the corresponding sides of the triangles.

Step 1: Compare the shorter leg

• Left triangle: $5$
• Right triangle: $\frac{25}{4}$

The scale factor is given by: $\text{Scale factor} = \frac{\frac{25}{4}}{5} = \frac{25}{4} \times \frac{1}{5} = \frac{25}{20} = \frac{5}{4}$

Step 2: Compare the longer leg

• Left triangle: $12$
• Right triangle: $15$

The scale factor for these sides is: $\text{Scale factor} = \frac{15}{12} = \frac{5}{4}$

Since both comparisons yield the same scale factor of $\frac{5}{4}$, we conclude that the scale factor between the triangles is 5/4.

Let me know if you'd like further details on the solution!

Here are 5 related questions to expand on this concept:

1. How do you calculate the area ratio between two similar triangles given the scale factor?
2. Can a triangle be similar to another if their scale factors are not constant across all sides?
3. How do scale factors apply to three-dimensional objects, like pyramids or cubes?
4. What happens to the perimeter of a triangle when the scale factor changes?
5. How do you determine the missing side of a right triangle if the scale factor and one side are known?

Tip: Always check all corresponding sides when calculating a scale factor to confirm consistency.