To find the scale factor of the side lengths of two similar squares when you know their areas, follow these steps:
1. Identify the areas of the squares:
- The area of the first square is [tex]\(16 \, \text{m}^2\)[/tex].
- The area of the second square is [tex]\(49 \, \text{m}^2\)[/tex].
2. Determine the side lengths of each square:
- The side length of a square is the square root of its area.
- For the first square:
[tex]\[
\text{Side length of square 1} = \sqrt{16 \, \text{m}^2} = 4 \, \text{m}
\][/tex]
- For the second square:
[tex]\[
\text{Side length of square 2} = \sqrt{49 \, \text{m}^2} = 7 \, \text{m}
\][/tex]
3. Find the scale factor:
- The scale factor between the side lengths of two similar figures is the ratio of their corresponding side lengths.
- Therefore, the scale factor from the first square to the second square is:
[tex]\[
\text{Scale factor} = \frac{\text{Side length of square 2}}{\text{Side length of square 1}} = \frac{7 \, \text{m}}{4 \, \text{m}} = 1.75
\][/tex]
So, the scale factor of the side lengths between these two similar squares is [tex]\(1.75\)[/tex].
