Question

the areas of two similar octagons are 9 m² and 25 m². what is the scale factor of their side lengths? ?:

Explanation:

Step1: Recall the ratio - area relationship

For two similar polygons, if the ratio of their areas is $A_1:A_2$, and the ratio of their corresponding side - lengths is $s_1:s_2$, then $\frac{A_1}{A_2}=(\frac{s_1}{s_2})^2$. Let $A_1 = 9$ and $A_2=25$.

Step2: Find the ratio of side - lengths

We have $(\frac{s_1}{s_2})^2=\frac{9}{25}$. Taking the square root of both sides, $\frac{s_1}{s_2}=\sqrt{\frac{9}{25}}$. Since side - lengths are non - negative, $\frac{s_1}{s_2}=\frac{3}{5}$.

Answer:

$3:5$