To solve this problem, we need to determine the scale factor between the two triangles. The scale factor is the ratio of the lengths of corresponding sides in similar triangles.

Step-by-Step Solution:

1. Identify Corresponding Sides:

   • The side of length 5 on the smaller triangle corresponds to the side of length $\frac{25}{4}$ on the larger triangle.

2. Calculate the Scale Factor:

   • The scale factor can be calculated as the ratio of the side length of the larger triangle to the side length of the smaller triangle.
   • Scale factor = $\frac{\text{Side length of larger triangle}}{\text{Side length of smaller triangle}}$

   For the given sides: $\text{Scale factor} = \frac{\frac{25}{4}}{5}$

3. Simplify the Scale Factor:

   • Simplify the expression: $\text{Scale factor} = \frac{25/4}{5} = \frac{25}{4} \times \frac{1}{5} = \frac{25}{20} = \frac{5}{4}$

   The scale factor is $\frac{5}{4}$.

Answer:

The scale factor of the right triangle on the right to the triangle on the left is $\frac{5}{4}$.

Would you like further details, or do you have any questions?

Additional Related Questions:

1. How do you find the scale factor if the triangles are reversed?
2. What is the perimeter of each triangle after scaling?
3. How does changing the scale factor affect the area of the triangles?
4. If the scale factor were $2$, what would the new side lengths be?
5. How can you determine if two triangles are similar using side lengths alone?

Tip: Always check that corresponding sides are proportional to confirm that triangles are similar.