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?

JKLM ~ NOPQ

JKLM = 8 16 12 24
NOPQ = 10 20 15 30

Answer 1

To find the scale factor of the similar polygons JKLM and NOPQ, we need to compare the corresponding side lengths.

### Given side lengths:
- For JKLM: 8, 16, 12, 24
- For NOPQ: 10, 20, 15, 30

### Step 1: Calculate the scale factor for the side lengths

The scale factor can be found by comparing any pair of corresponding sides. We can take the ratio of the sides from JKLM to NOPQ.

For example:
- For the first pair: \( \text{Scale factor} = \frac{10}{8} = 1.25 \)
- For the second pair: \( \text{Scale factor} = \frac{20}{16} = 1.25 \)
- For the third pair: \( \text{Scale factor} = \frac{15}{12} = 1.25 \)
- For the fourth pair: \( \text{Scale factor} = \frac{30}{24} = 1.25 \)

Since all ratios give the same value, the scale factor of the polygons is:

\[
\text{Scale factor} = 1.25
\]

### Step 2: Scale factor of their perimeters

The scale factor of the perimeters is the same as the scale factor of the side lengths:

\[
\text{Scale factor of perimeters} = 1.25
\]

### Step 3: Scale factor of their areas

The scale factor for areas is the square of the scale factor for the side lengths:

\[
\text{Scale factor of areas} = (\text{Scale factor})^2 = (1.25)^2 = 1.5625
\]

### Summary
- Scale factor of the polygons: **1.25**
- Scale factor of their perimeters: **1.25**
- Scale factor of their areas: **1.5625**