Final answer:
The scale factor of the side lengths of the two similar squares is 2.
Step-by-step explanation:
To find the scale factor of the side lengths, we need to compare the areas of the two similar squares. The area of the first square is 16m^2 and the area of the second square is 49m^2. We can use the formula for the area of a square, which is side length squared, to find the side lengths of the squares.
Let the side length of the first square be x. Then, the side length of the second square is 2x (twice the length of the first square).
We can set up the equation x^2 = 16 to find the side length of the first square. Solving for x, we get x = 4. Therefore, the side length of the second square is 2 * 4 = 8.
The scale factor is the ratio of the side lengths of the two squares: 8/4 = 2. So, the scale factor of their side lengths is 2.