Octagon Scale 5Eeeac

1. **State the problem:** We have two similar octagons with areas $4$ m² and $25$ m². We need to find the scale factor of their side lengths. 2. **Recall the formula:** For similar figures, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. If $k$ is the scale factor of side lengths, then: $$\frac{\text{Area}_1}{\text{Area}_2} = k^2$$ 3. **Apply the given values:** $$\frac{4}{25} = k^2$$ 4. **Solve for $k$:** $$k = \sqrt{\frac{4}{25}} = \frac{\sqrt{4}}{\sqrt{25}} = \frac{2}{5}$$ 5. **Interpretation:** The scale factor of the side lengths is $\frac{2}{5}$ or $0.4$. This means each side length of the smaller octagon is $0.4$ times the corresponding side length of the larger octagon.