Final answer:
To find the perimeter of the smaller polygon, we can set up a proportion using the ratio of the side lengths. The perimeter of the larger polygon is 280 inches and the ratio of the side lengths is 1/7. So, the perimeter of the smaller polygon is 40 inches.
Step-by-step explanation:
To find the perimeter of the smaller polygon, we'll need to use the ratio of the side lengths and the perimeter of the larger polygon. Let's assume that the perimeter of the smaller polygon is P. The ratio of the side lengths is 1/7, which means that the side length of the smaller polygon is 1/7th of the side length of the larger polygon. Let's denote the side length of the larger polygon as L. We can set up a proportion:
L/7 = P
Now, we know that the perimeter of the larger polygon is 280 inches, so we substitute L with 280:
280/7 = P
Simplifying the equation, we get:
P = 40 inches
Therefore, the perimeter of the smaller polygon is 40 inches.