Question

The perimeters of two similar polygons are 20 and 28. One side of the smaller polygon is 4. Find the corresponding side of the larger polygon.

Answer 1

The ratio of the perimeters of the polygons are exactly the same as the ratio of their similarities. It's only the area ratios and the volume ratios that change. Perimeter is a one-to-one. Area is a squared-to-squared, and volume is a cubed-to-cubed. So once you fill in your ratio proportions, you have the missing side.

Answer 2

Number of sides in the polygon = 20/4 = 5. Polygons are similar so the length of its side = 28/5 = 5.6

Answer 3

Here is the ratio set-up\[\frac{ 20 }{ 24 }=\frac{ 4 }{ x }\]You have the perimeter of the smaller on top and the perimeter of the larger on the bottom. You have then the side length of the smaller on top (smaller on top for both and larger on bottom for both. You could do larger on top as long as you keep larger with larger and smaller with smaller either on the top or the bottom of the fraction.) Cross-multiply then to find x.