Final answer:
The scale factor for the side lengths of two similar octagons with areas 4m^2 and 9m^2 is 1.5, derived from taking the square root of the ratio of their areas.
Step-by-step explanation:
The area of similar figures is related to the square of their scale factor. For the given octagons with areas 4m2 and 9m2, we need to find the scale factor that relates their side lengths. Since area scales as the square of the scale factor, we can find the ratio of their areas and take the square root to find the scale factor of their side lengths.
The ratio of their areas is 9/4, which when simplified as a fraction is 2.25. We can now take the square root of this ratio to find the actual scale factor for the side lengths.
The square root of 2.25 is 1.5, indicating that the side lengths of the larger octagon are 1.5 times longer than those of the smaller octagon.