Question

polygon p is a scaled copy of polygon n.
diagrams: polygon n (sides: top=4, left=8, bottom=16, right=4); polygon p (sides: top=10, left=20, bottom=40, right=10)
what scale factor takes polygon n to polygon p?

Explanation:

Step1: Identify corresponding sides

Choose a pair of corresponding sides from polygon N and polygon P. For example, the top horizontal side of N is 4, and of P is 10. Or the bottom horizontal side: N is 16, P is 40. Or the left vertical side: N is 8, P is 20. Or the right vertical side: N is 4, P is 10.

Step2: Calculate scale factor

Scale factor is the ratio of the length of a side in P to the corresponding side in N. Let's use the top horizontal sides: $\frac{10}{4} = 2.5$, or bottom horizontal: $\frac{40}{16} = 2.5$, left vertical: $\frac{20}{8} = 2.5$, right vertical: $\frac{10}{4} = 2.5$. All give the same ratio.

Answer:

2.5