This problem involves scale factors, as Polygon B is a scaled-down version of Polygon A. To solve for $c$, we use the fact that corresponding sides of similar polygons are proportional.

We know the following sides:

• Polygon A: height = 35, width = 15
• Polygon B: height = 8, width = 6

The scale factor between the polygons can be calculated by comparing the corresponding sides. Let's use the widths to calculate the scale factor:

$\text{Scale factor} = \frac{\text{Width of Polygon B}}{\text{Width of Polygon A}} = \frac{6}{15} = \frac{2}{5}$

Now, apply this scale factor to find $c$, the corresponding side in Polygon B, using the side length of 35 from Polygon A:

$c = \text{Scale factor} \times \text{Height of Polygon A} = \frac{2}{5} \times 35 = 14$

Thus, $c = 14$.

Would you like more details on how I arrived at this solution? Here are some related questions to explore:

1. How do you verify the similarity of two polygons?
2. How can you use scale factors to solve other types of geometry problems?
3. What happens if the scale factor is greater than 1?
4. How do area and volume scale in proportion to linear dimensions?
5. Can you use a different pair of corresponding sides to calculate the scale factor?

Tip: Always ensure that you match corresponding sides correctly when calculating scale factors.