Answer:
Perimeter of polygon B = 80 units
Step-by-step explanation:
Since both polygons are similar, their corresponding sides and perimeters are proportional. Knowing this we can setup a proportion to find the perimeter of polygon B.
![\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}](https://tex.z-dn.net/?f=%5Cfrac%7Bside-polygonA%7D%7Bside-polygonB%7D%20%3D%5Cfrac%7Bperimeter-polygonA%7D%7Bperimeter-polygonB%7D)
Let
be the perimeter of polygon B. We know from our problem that the side of polygon A is 24, the side of polygon B is 15, and the perimeter of polygon A is 128.
Let's replace those value sin our proportion and solve for
:
![\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}](https://tex.z-dn.net/?f=%5Cfrac%7Bside-polygonA%7D%7Bside-polygonB%7D%20%3D%5Cfrac%7Bperimeter-polygonA%7D%7Bperimeter-polygonB%7D)
![\frac{24}{15} =\frac{128}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B15%7D%20%3D%5Cfrac%7B128%7D%7Bx%7D)
![x=\frac{128*15}{24}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B128%2A15%7D%7B24%7D)
![x=\frac{1920}{24}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1920%7D%7B24%7D)
![x=80](https://tex.z-dn.net/?f=x%3D80)
We can conclude that the perimeter of polygon B is 80 units.