To find the scale factor between the two triangles, we compare the lengths of their corresponding sides.

In the image:

• The smaller triangle has two given sides: 5 and 5.
• The larger triangle has two corresponding sides: 7 and 7.

The scale factor is the ratio of the sides of the larger triangle to the corresponding sides of the smaller triangle.

Thus, the scale factor is:

$\frac{7}{5}$

This is already in its simplest form.

So, the scale factor is $\frac{7}{5}$.

Would you like more details or have any questions?

Here are five related questions for further practice:

1. If the area of the smaller triangle is 12.5 square units, what is the area of the larger triangle?
2. If the hypotenuse of the smaller triangle is $x$, what would be the hypotenuse of the larger triangle?
3. What would the perimeter of each triangle be?
4. If another triangle is scaled by a factor of $\frac{3}{2}$, how would its sides compare to the original smaller triangle?
5. How do the angles of the two triangles compare?

Tip: When working with similar triangles, the ratio of corresponding sides is constant across all sides.