Question

What is the scale factor of the similar polygons below?
What is the scale factor of their perimeters?
What is the scale factor of their areas?

ABCDE ~ FGHIJ

ABCDE = 10, 6, 8, 6, 2

FGHIJ = 5, 3, 4, 3, 1

Answer 1

To find the scale factor of the similar polygons \(ABCDE\) and \(FGHIJ\), we can compare the lengths of corresponding sides.

First, let's find the sides of each polygon:

- For \(ABCDE\), the sides are: \(10, 6, 8, 6, 2\)
- For \(FGHIJ\), the sides are: \(5, 3, 4, 3, 1\)

Now we can find the scale factor:

1. Comparing the corresponding sides:
- For side \(10\) (from \(ABCDE\)) and \(5\) (from \(FGHIJ\)):
\[
\text{Scale Factor} = \frac{10}{5} = 2
\]
- For side \(6\) and \(3\):
\[
\text{Scale Factor} = \frac{6}{3} = 2
\]
- For side \(8\) and \(4\):
\[
\text{Scale Factor} = \frac{8}{4} = 2
\]
- For side \(6\) and \(3\):
\[
\text{Scale Factor} = \frac{6}{3} = 2
\]
- For side \(2\) and \(1\):
\[
\text{Scale Factor} = \frac{2}{1} = 2
\]

The scale factor for the sides of the polygons is consistent across all pairs, therefore the scale factor is \(2\).

### Scale Factor of Perimeters
The scale factor for the perimeters of similar polygons is the same as the scale factor of their corresponding sides. Hence:

\[
\text{Scale Factor (Perimeters)} = 2
\]

### Scale Factor of Areas
The scale factor for the areas of similar polygons is the square of the scale factor of their corresponding sides. Therefore:

\[
\text{Scale Factor (Areas)} = (\text{Scale Factor})^2 = 2^2 = 4
\]

### Summary
1. Scale factor of the polygons: \(2\)
2. Scale factor of their perimeters: \(2\)
3. Scale factor of their areas: \(4\)