Question

max is finding the perimeter of different - sized equilateral triangles. there is a proportional relationship between the side length of the equilateral triangle in feet, x, and the perimeter of the equilateral triangle in feet, y. what is the constant of proportionality? write your answer as a whole number or decimal.

x (side length in feet)	y (perimeter in feet)
8	24
9	27
10	30

feet in perimeter per foot in side length

Explanation:

Step1: Recall the formula for perimeter of equilateral triangle

For an equilateral triangle, the perimeter $y$ is related to the side - length $x$ by the formula $y = 3x$. The constant of proportionality $k$ in the direct - variation equation $y=kx$ can be found by dividing $y$ by $x$.

Step2: Calculate the constant of proportionality

Take any pair of values from the table. For example, when $x = 5$ and $y = 15$, then $k=\frac{y}{x}=\frac{15}{5}=3$. We can check with other pairs: when $x = 8$, $y = 24$, and $\frac{y}{x}=\frac{24}{8}=3$; when $x = 9$, $y = 27$, and $\frac{y}{x}=\frac{27}{9}=3$; when $x = 10$, $y = 30$, and $\frac{y}{x}=\frac{30}{10}=3$.

Answer:

3