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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.

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.

Learn how to find the scale factor between two similar right triangles. The problem compares the corresponding sides and simplifies the ratio. Ideal for students in Grades 8-10 studying geometry and proportionality in triangles.

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