The shortest sides of two similar polygons have lengths in the ratio 2: 5. the perimeter of the smaller polygon is 20. the perimeter of the larger polygon is

A similar triangle has the same ratio on every side, so that means the perimeter has the same ratio as well. 
Set up the proportion: 2/5 = 20/x
multiply the means and extremes to get
2x = 100
divide both sides by 2
x = 50
The perimeter of the larger polygon is 50
Hope this helped =)