To find the scale factor between two similar triangles, you can compare the lengths of corresponding sides. Here, the left triangle has sides of length 17, while the right triangle has sides of length $51/2$.

The scale factor can be determined by dividing the side length of the larger triangle by the side length of the smaller triangle. Using the provided values:

$\text{Scale factor} = \frac{51/2}{17}$

Let's simplify this fraction to find the scale factor in simplest form.The scale factor between the two triangles is $\frac{3}{2}$.

Would you like any details on this calculation or have any other questions? Here are some related questions you might consider:

1. How would the calculation change if different sides were used?
2. What is the area ratio between the two triangles?
3. How would you verify that the triangles are indeed similar?
4. Can you find a real-world example where scale factors are used?
5. How does the concept of scale factor apply to other geometric shapes?

Tip: Remember that in similar figures, not only are the sides proportional, but the ratios of areas are the square of the scale factor.