Answer:
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
Area of Octagon A = 4 m²
Side length of Octagon A = a
Area of Octagon B = 9 m²
Side length of Octagon B = b
The scale factor of their side lengths = [tex] \frac{a}{b} [/tex]
According to the area of similar polygons theorem, [tex] \frac{4}{9} = (\frac{a}{b})^2 [/tex]
Thus,
[tex] \sqrt{\frac{4}{9}} = \frac{a}{b} [/tex]
[tex] \frac{\sqrt{4}}{\sqrt{9}} = \frac{a}{b} [/tex]
[tex] \frac{2}{3} = \frac{a}{b} [/tex]
Scale factor of their sides = [tex] \frac{2}{3} [/tex]
