In an equilateral triangle, all three sides are of equal length. The perimeter $P$ of the triangle is the sum of the lengths of its three sides, so for an equilateral triangle with side length $S$, the perimeter $P$ is given by:

$P = S + S + S = 3S$

This equation indicates that the perimeter is always three times the length of one side of the triangle.

To graph this:

You are graphing the relationship between the perimeter $P$ and the side length $S$, which is described by the equation $P = 3S$. This is a simple linear equation where:

• $P$ is the dependent variable (y-axis),
• $S$ is the independent variable (x-axis).

Steps for Graphing:

1. Choose some values of $S$ (e.g., 1, 2, 3, 4, etc.).
2. For each value of $S$, calculate the corresponding $P$ using the equation $P = 3S$.
3. Plot the points $(S, P)$ on the graph.
4. Draw a straight line through the points, as the equation represents a linear relationship.

Here is a table of values to plot:

$S$	$P = 3S$
1	3
2	6
3	9
4	12
5	15

This will give you a straight line with a slope of 3.

Would you like a graph plotted for this, or any further clarification?

Relative Questions:

1. How does changing the side length affect the perimeter of an equilateral triangle?
2. What happens to the perimeter if the side length doubles?
3. How does the graph of $P = 3S$ compare to other linear functions like $P = 2S$?
4. Can you derive the formula for the area of an equilateral triangle using its side length?
5. What is the geometric significance of a slope in the context of this graph?

Tip: In an equilateral triangle, each angle is always 60°, and the symmetry of the triangle simplifies many geometric properties.