When dealing with similar polygons, the ratio of their corresponding side lengths is directly proportional to the ratio of their perimeters. This means that the ratio of the perimeters of two similar polygons is the same as the ratio of their corresponding side lengths.
Given that the ratio of the corresponding side lengths of two similar polygons is [tex]\( \frac{5}{9} \)[/tex], we can directly use this ratio for the perimeters as well.
Therefore, the ratio of the perimeters of these two similar polygons is also [tex]\( \frac{5}{9} \)[/tex].
To match this with the given choices:
A. 5:9
B. 10:9
C. 25:81
D. 10:81
The correct answer is:
A. 5:9
