Question

this table shows the relationship between the diagonal length and perimeter of an octagon. how can you tell if two quantities in a geometry situation are proportional?

Explanation:

Step1: Calculate the ratio of perimeter to diagonal length

For diagonal length \(d = 1\) and perimeter \(P=3.06\), the ratio is \(\frac{P}{d}=\frac{3.06}{1}=3.06\)
For \(d = 2\) and \(P = 6.12\), \(\frac{P}{d}=\frac{6.12}{2}=3.06\)
For \(d = 3\) and \(P=9.18\), \(\frac{P}{d}=\frac{9.18}{3}=3.06\)
For \(d = 4\) and \(P = 12.24\), \(\frac{P}{d}=\frac{12.24}{4}=3.06\)

Answer:

Two quantities in a geometry situation are proportional if the ratio of one quantity to the other quantity is a constant. In this case, since \(\frac{\text{Perimeter}}{\text{Diagonal Length}}=3.06\) (a constant) for all the given values in the table, the diagonal length and perimeter of the octagon are proportional.