Question

Write a formula and graph the formula of the following problem.The perimeter P of an equilateral triangle equals three times the length of a size s.

Answer 1

The formula for the perimeter of an equilateral triangle is P = 3s. To graph this, a line with a slope of 3 is drawn on a coordinate system with side length s along the x-axis and perimeter P along the y-axis.

Step-by-step explanation:

The question pertains to the perimeter of an equilateral triangle. In mathematics, the perimeter of a geometric figure is the total length of its boundary. For an equilateral triangle where all three sides are of equal length, the perimeter P can be found by multiplying the length of one side s by 3. Therefore, the formula for the perimeter is P = 3s.

To graph this relationship, we can use a two-dimensional coordinate system with P on the y-axis and s on the x-axis. Each point (s, P) on the graph represents a different equilateral triangle, with side length s and perimeter P. The graph will be a straight line that passes through the origin (0,0), since a triangle with side length 0 will also have a perimeter of 0. This line will have a slope of 3, indicating that for every unit increase in side length s, the perimeter P increases by three units.

To relate this to other shapes, consider a square with side length a where the perimeter is 4a and the area is a². For a cube, the volume is a³. These relationships are fundamental in geometry, as they link linear dimensions with measures of perimeter, area, and volume. The same concept applies here to the equilateral triangle, linking the side length s with the perimeter P.

Answer 2

The perimeter of the equilateral triangle is represented as P. The perimeter is equal to three times the length of the side s of the equilateral triangle, which is written as 3s. Hence, we can write the formula of the equilateral triangle as

`P=3s`

Now, to plot this formula, we need to find ordered pairs. This can be done by letting some values of s and evaluating the equation above to solve for P. The resulting pairs are represented as (s, P) which can now be plotted in the Cartesian Coordinate plane.

In this problem, I will use s = 1, 2, and 3. We will have the following values of P and coordinate pairs.

`\begin{gathered} P_1=3(1)=3\rightarrow\rightarrow(1,3)_{} \\ P_2=3(2)=6\rightarrow\rightarrow(2,6) \\ P_3=3(3)=9\rightarrow\rightarrow(3,9) \end{gathered}`

We can now plot the coordinate points on the Cartesian coordinate plane as

Drawing a line connecting the dots, the graph of the formula is represented as