The areas of two similar octagons are \( 4 \mathrm{~m}^{2} \) and \( 25 \mathrm{~m}^{2} \) What is the scale factor of their side lengths? \[ \text { [?]: [ ] } \]

To find the scale factor of their side lengths, we can use the ratio of their areas. The ratio of the areas of two similar figures is equal to the square of the scale factor of their corresponding side lengths. Given that the areas are \( 4 \mathrm{~m}^{2} \) and \( 25 \mathrm{~m}^{2} \), we can set up the equation: \[ \frac{4}{25} = k^2 \] where \( k \) is the scale factor. Taking the square root of both sides gives us: \[ k = \sqrt{\frac{4}{25}} = \frac{2}{5} \] So, the scale factor of their side lengths is \( \frac{2}{5} \). \[ \text { Scale Factor: } \frac{2}{5} \]