The problem asks for the scale factor that takes parallelogram $H$ to parallelogram $I$.

Given:

• Parallelogram $H$ has sides 35 and 15.
• Parallelogram $I$ has sides 28 and 12.

The scale factor can be determined by comparing corresponding sides. Let's take the shorter sides of both parallelograms first. The ratio of the shorter side of parallelogram $I$ to parallelogram $H$ is:

$\text{Scale factor} = \frac{12}{15} = \frac{4}{5}$

To confirm, let's check if the ratio of the longer sides also matches:

$\frac{28}{35} = \frac{4}{5}$

Since both sides scale by the same factor, the scale factor from parallelogram $H$ to parallelogram $I$ is $\frac{4}{5}$ or 0.8.

Would you like a detailed explanation of how scaling works or have any questions?

Here are some related questions:

1. What is the reverse scale factor from parallelogram $I$ to parallelogram $H$?
2. How do we apply scale factors to areas of parallelograms?
3. What is the perimeter of parallelogram $I$ given the scale factor?
4. How does the concept of similarity apply to other polygons, like triangles?
5. How can you determine the scale factor if only areas of the shapes are given?

Tip: Always check both corresponding sides to confirm the scale factor matches.