Chapter 5.2, Problem 16P

An equilateral triangle is a triangle with three equal sides. The perimeter of an equilateral triangle varies directly with the length of one side. What is an equation that relates the perimeter $p$ and length $l$ of a side? What is the graph of the equation?

To determine

To determine the equation and the graph it.

Explanation of Solution

Given:

The perimeter of an equilateral triangle is p .

The length of each side is l.

Calculation for graph:

The sum of all sides of a triangle is equal to the perimeter of a triangle.

The length of all sides of a equilateral triangle is same.

Thus,

  $\begin{array}{l}\Rightarrow p=l+l+l\\ \Rightarrow p=3l\end{array}$

Hence, the required equation is $p=3l$.

Graph:

  

Interpretation:

From the graph it can be observed that the horizontal extent of the graph is from$-\infty$ to $\infty$.

And the vertical extent of the graph is also from$-\infty$ to $\infty$.

So, both the domain and range of the function is$(-\infty ,\infty )$.