The sides of a polygon are 3, 5, 4, and 6. the shortest side of a similar polygon is 9. find the ratio of their perimeters.

The smallest side of the first polygon is 3 units. The shortest side of the second polygon is 9 units.

9 is a factor of 3. So the ratio between the smallest sides of each polygon is:

1 : 3

If the smallest side of each polygon have a ratio of 1 : 3, then the other sides will have a ratio of 1 : 3 (considering that the polygons are 'similar').

Therefore, their perimeters will have the same ratio. Thus the ratio of the two polygons' perimeter is:

1 : 3