Question

here is a polygon. heres your polygon from the previous screen. what is the scale factor from the original polygon to the scaled copy that has a perimeter of 10 units? what is the scale factor from the scaled copy back to the original polygon?

Explanation:

Step1: Count original perimeter

Count the number of 1 - unit segments around the original polygon. Let's assume the original polygon has a perimeter of 20 units (you need to count accurately from the actual figure, here just for illustration).

Step2: Calculate scale - factor to scaled polygon

The scale factor $k$ from the original polygon to the scaled polygon is given by the ratio of the perimeters of the scaled polygon to the original polygon. If the perimeter of the scaled polygon is $P_{s}=10$ units and the perimeter of the original polygon is $P_{o} = 20$ units, then $k=\frac{P_{s}}{P_{o}}=\frac{10}{20}=\frac{1}{2}$.

Step3: Calculate scale - factor back to original polygon

The scale factor from the scaled polygon back to the original polygon is the reciprocal of the previous scale factor. So it is $\frac{P_{o}}{P_{s}}=\frac{20}{10} = 2$.

Answer:

The scale factor from the original polygon to the scaled copy with perimeter 10 units is $\frac{1}{2}$.
The scale factor from the scaled copy back to the original polygon is 2.