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This problem involves similar polygons, as polygon \( B \) is a scaled copy of polygon \( A \). Since they are similar, the ratio of corresponding sides between the two polygons remains the same.

Given:
- Side lengths of Polygon \( A \): 15, 35, and 20.
- Side lengths of Polygon \( B \): 6, \( c \), and 8.

We will find the scale factor between the two polygons by comparing corresponding side lengths.

### Step 1: Find the scale factor.
The side corresponding to 15 in Polygon \( A \) is 6 in Polygon \( B \). Thus, the scale factor \( k \) is:

\[
k = \frac{6}{15} = \frac{2}{5}
\]

### Step 2: Find the value of \( c \).
To find the value of \( c \), we use the fact that the corresponding side in Polygon \( A \) is 35. Since the scale factor is \( \frac{2}{5} \), we can set up the proportion:

\[
\frac{c}{35} = \frac{2}{5}
\]

### Step 3: Solve for \( c \).

\[
c = 35 \times \frac{2}{5} = 14
\]

Thus, the value of \( c \) is \( 14 \).

Would you like more details on how we used similarity in this problem?

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Here are 5 related questions for further exploration:
1. If the area of Polygon \( A \) is given, how would you find the area of Polygon \( B \)?
2. What is the perimeter of Polygon \( B \) if the perimeter of Polygon \( A \) is known?
3. How do the angles of two similar polygons compare?
4. Can you calculate the scale factor by comparing the height (20 and 8) instead of the base?
5. If polygon \( B \) had a different scale factor, how would it affect the side lengths?

**Tip**: In similar polygons, not only the sides but also the ratios of areas follow a squared relationship with the scale factor!

Polygon B is a scaled copy of polygon A. What is the value of c?

Learn how to find the missing side length of a polygon by using proportions and scale factors. This problem involves two similar polygons where polygon B is a scaled copy of polygon A. The solution involves finding the corresponding side length using the similarity theorem for polygons. Suitable for Grades 6-8 students.

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