Answer:
[tex] \frac{3}{5} [/tex]
Step-by-step explanation:
Let the side length for the octagon having 9m² as area = x
Side length for the octagon having area of 25m² = y.
Thus:
[tex] \frac{9}{25} = (\frac{x}{y})^2 [/tex] (area of similar polygons theorem)
The scale factor of their sides would be [tex] \frac{x}{y} [/tex]. Which is:
[tex] \sqrt{\frac{9}{25}} = \frac{x}{y} [/tex]
[tex] \frac{\sqrt{9}}{\sqrt{25}} = \frac{x}{y} [/tex]
[tex] \frac{3}{5} = \frac{x}{y} [/tex]
Scale factor of their sides = [tex] \frac{3}{5} [/tex]
