Question

eva is finding the perimeter of different - sized regular pentagons. there is a proportional relationship between the side length of the regular pentagon in inches, x, and the perimeter of the regular pentagon in inches, y.

x (side length in inches)	y (perimeter in inches)
4	20
8	40
12	60

what is the constant of proportionality? write your answer as a whole number or decimal. inches in perimeter per inch in side length

Explanation:

Step1: Recall the formula for proportionality

For a proportional relationship $y = kx$, $k$ is the constant of proportionality. We can find $k$ by dividing $y$ by $x$.

Step2: Choose a pair of values from the table

Let's take the first - pair $x = 2$ and $y = 10$.
$k=\frac{y}{x}$

Step3: Calculate the constant of proportionality

Substitute $x = 2$ and $y = 10$ into the formula: $k=\frac{10}{2}=5$.
We can check with other pairs. For $x = 4$ and $y = 20$, $k=\frac{20}{4}=5$; for $x = 8$ and $y = 40$, $k=\frac{40}{8}=5$; for $x = 12$ and $y = 60$, $k=\frac{60}{12}=5$.

Answer:

5