We are given that two rectangles are similar and have a scale factor of 2:4. Note that it can be rewritten as a fraction and simplified.
2/4= 1/2Now we want to find the perimeter of the small rectangle, P_s. Recall that if two polygons are similar, their perimeters are proportional to the scale factor between them. We are given that the perimeter of the large rectangle is 80 meters, so we can write the following proportion.
P_s/80=1/2
Finally, we can solve this equation to find the perimeter of the smaller rectangle.
Two polygons are similar if and only if their corresponding angles are congruent and corresponding side lengths are proportional.
In other words similar polygons have the same shape but can have different sizes. Additionally, each pair of similar figures has its scale factor, which is the ratio of the lengths of the corresponding sides.
