Question

problem 6
an equilateral triangle is a triangle where all three sides have the
same length.
the table from a previous screen is shown.
what is a constant of proportionality for the relationship?

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \(y = kx\), the constant of proportionality \(k=\frac{y}{x}\)

Step2: Substitute values from the table

Let \(x\) be side - length and \(y\) be perimeter.
Take the first pair: \(x = 3,y=9\), then \(k=\frac{y}{x}=\frac{9}{3}\)
Take the second pair: \(x = 10,y = 30\), then \(k=\frac{y}{x}=\frac{30}{10}\)
Take the third pair: \(x=27,y = 81\), then \(k=\frac{y}{x}=\frac{81}{27}\)
Take the fourth pair: \(x = 105,y=315\), then \(k=\frac{y}{x}=\frac{315}{105}\)

Step3: Calculate the value of \(k\)

\(\frac{9}{3}=3\), \(\frac{30}{10}=3\), \(\frac{81}{27}=3\), \(\frac{315}{105}=3\)

Answer:

\(3\)