If the areas of two similar geometric polygons are in the ratio of 25 : 64, what is the ratio of their corresponding sides?

The correct option is 5 : 8.

Step-by-Step Explanation:

According to the geometric properties of similar figures, the ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths.

If $s_1$ and $s_2$ represent the corresponding side lengths of the two similar polygons, and $A_1$ and $A_2$ represent their respective areas, the relationship is given by the formula:

$\frac{A_1}{A_2}={\left(\frac{s_1}{s_2}\right)}^2$

We are given that the ratio of their areas is 25 : 64, which can be written as a fraction:

$\frac{A_1}{A_2}=\frac{25}{64}$

Substituting this ratio into the formula:

$\frac{25}{64}={\left(\frac{s_1}{s_2}\right)}^2$

To find the ratio of their corresponding sides $\frac{s_1}{s_2}$, take the square root of both sides of the equation:

$\frac{s_1}{s_2}=\sqrt{\frac{25}{64}}$

$\frac{s_1}{s_2}=\frac{\sqrt{25}}{\sqrt{64}}$

$\frac{s_1}{s_2}=\frac{5}{8}$

Therefore, the ratio of their corresponding sides is 5 : 8.