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.
(3+4+5+6)/(9+12+15+18) =
1/3
To find the ratio of the perimeters of two similar polygons, we need to compare the lengths of corresponding sides.
In this case, we have a polygon with sides 3, 5, 4, and 6, and a similar polygon with a shortest side of 9.
To find the corresponding sides, we need to multiply each side length of the first polygon by the same scaling factor. In this case, we can find the scaling factor by dividing the shortest side of the second polygon (9) by the shortest side of the first polygon.
Scaling factor = Length of shortest side of second polygon / Length of shortest side of first polygon = 9 / 3 = 3
Now, we can multiply each side length of the first polygon by the scaling factor to find the corresponding sides of the second polygon:
Corresponding sides of the second polygon = Scaling factor * Corresponding sides of the first polygon
= 3 * {3, 5, 4, 6}
= {9, 15, 12, 18}
Now, we can calculate the perimeters of both polygons by adding up the side lengths.
Perimeter of the first polygon = 3 + 5 + 4 + 6 = 18
Perimeter of the second polygon = 9 + 15 + 12 + 18 = 54
The ratio of their perimeters is given by:
Ratio of perimeters = Perimeter of the second polygon / Perimeter of the first polygon = 54 / 18 = 3
Therefore, the ratio of their perimeters is 3:1.