Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is $\
frac{2}{5}$
. Find the perimeter of the other polygon.
The perimeter of the other polygon is
meters.
1 answer:
Answer:
The perimeter of the other polygon is ![34\ m](https://tex.z-dn.net/?f=34%5C%20m)
Step-by-step explanation:
we know that
If two figures are similar, then the ratios of its perimeter is equal to the scale factor
Let
z---> the scale factor
x----> the perimeter of the other polygon
y----> the perimeter of the larger polygon
so
![z=\frac{x}{y}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx%7D%7By%7D)
we have
![z=\frac{2}{5}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B2%7D%7B5%7D)
![y=85\ m](https://tex.z-dn.net/?f=y%3D85%5C%20m)
substitute and solve for x
![y=85*(2/5)=34\ m](https://tex.z-dn.net/?f=y%3D85%2A%282%2F5%29%3D34%5C%20m)
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