Question

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 $square$ meters.

Explanation:

Step1: Relate side ratio to perimeter ratio

For similar polygons, the ratio of perimeters equals the ratio of corresponding side lengths. The ratio $\frac{2}{5}$ means the smaller polygon's perimeter is $\frac{2}{5}$ of the larger one.

Step2: Calculate smaller polygon's perimeter

Multiply larger perimeter by the ratio.
$\text{Smaller Perimeter} = 85 \times \frac{2}{5}$

Answer:

34 meters