SOLUTION: Polygon R and polygon S are similar. The perimeter of polygon R is 192 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 3 cm, what is the length of the corr

Algebra ->  Polygons -> SOLUTION: Polygon R and polygon S are similar. The perimeter of polygon R is 192 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 3 cm, what is the length of the corr      Log On


   

Question 1100371: Polygon R and polygon S are similar. The perimeter of polygon R is 192 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 3 cm, what is the length of the corresponding side in polygon R?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
For similar polygons, the ratio of the lengths of their corresponding sides is the same as the ratio of their perimeters.


Therefore, you have this PROPORTION:


x%2F3 = 192%2F36.


It gives you  x = %28192%2A3%29%2F36 = 16.


Answer.  The length of the corresponding side in polygon R is 16 cm.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Polygon S has side length 3cm and perimeter 36cm; so it has 36/3 = 12 sides.

If polygon R is similar, then it too has 12 sides. If its perimeter is 192cm, then the length of each side is 192/12 = 16cm.


Sorry.... That solution assumes the polygons are regular polygons. The statement of the problem didn't say that. So we have to use a different method for solving the problem.

The problem only talks about one side of polygon R and the corresponding side of polygon S.
We are given that the perimeters of the polygons are 36 and 192, so the ratio of similarity is 36:192 = 3:16.
Since the polygons are similar, the ratio of any corresponding measurements of length will be that same 3:16.
So if a side of the smaller polygon is 3cm, the corresponding side of the larger polygon is 16cm.