Question

1. the equation ( p = 3s ) represents the perimeter ( p ) of an equilateral triangle with side length ( s ). is there a proportional relationship between the perimeter and the side length of an equilateral triangle? explain.

Explanation:

Step1: Recall the definition of proportional relationship

A proportional relationship is of the form \(y = kx\), where \(k\) is a constant (the constant of proportionality).

Step2: Analyze the given equation \(P = 3s\)

Here, \(P\) (perimeter) is like \(y\), \(s\) (side - length) is like \(x\), and the constant \(k = 3\). When \(s = 0\), \(P=3\times0 = 0\) (the graph passes through the origin \((0,0)\)).

Answer:

Yes, there is a proportional relationship. The equation \(P = 3s\) is in the form \(y=kx\) (where \(y = P\), \(x = s\), and \(k = 3\)), and when \(s = 0\), \(P = 0\). So the perimeter \(P\) and side - length \(s\) of an equilateral triangle have a proportional relationship.