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 proportional - relationship definition

A proportional relationship between two variables $y$ and $x$ can be written in the form $y = kx$, where $k$ is a non - zero constant of proportionality.

Step2: Analyze the given equation

The equation for the perimeter $P$ of an equilateral triangle is $P = 3s$, where $P$ is the perimeter and $s$ is the side length. Here, $k = 3$ (a non - zero constant). When $s$ increases, $P$ increases in such a way that the ratio $\frac{P}{s}=3$ always holds.

Answer:

Yes, there is a proportional relationship between the perimeter and the side length of an equilateral triangle because the equation $P = 3s$ is in the form $y = kx$ (where $y = P$, $x = s$, and $k = 3$), and the ratio of the perimeter to the side length is a non - zero constant ($3$).