Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is (2)/(5). Find the perimeter of the other polygon.

Question

Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is
`(2)/(5)`. Find the perimeter of the other polygon.

Answer 1

Suppose the polygons have 3 sides,
`s_1,s_2,s_3`. In the smaller polygon, the corresponding sides would have lengths
`\frac25s_1,\frac25s_2,\frac25s_3`.

So if the perimeter of the larger polygon is

`s_1+s_2+s_3=85`

then the perimeter of the smaller polygon would be

`\frac25(s_1+s_2+s_3)=\frac25\cdot85`

so its perimeter would be 34 meters.