In the diagram below what is the relationship between the number of triangles and the perimeter of the figure they form? Represent this relationship using a table, words, an equation, and a graph Let x-the number of triangles Let y the perimeter of the figure
4, 4, 5 1 triangle 5,4,5,4 2 triangle 4,5,4,5,5 3 triangle
Represent the relationship using a table. Complete the table below.
Number of Triangles, x Perimeter, y Ordered Pair (xy)
1
2
3
(Simplify your answers)
Number of Triangles, x Perimeter, y Ordered Pair (xy)
1 14 (1, 14)
2 18 (2, 18)
3 22 (3, 22)
To represent the relationship between the number of triangles and the perimeter of the figure in a table, you can complete the table as follows:
Number of Triangles, x | Perimeter, y | Ordered Pair (xy)
1 | 13 | (1, 13)
2 | 18 | (2, 18)
3 | 23 | (3, 23)
In this table, the number of triangles (x) represents the independent variable, while the perimeter (y) represents the dependent variable. Each ordered pair (xy) represents a specific combination of the number of triangles and the corresponding perimeter.
To find the relationship between the number of triangles and the perimeter of the figure they form, we can analyze the given information.
1 triangle has a perimeter of 4.
2 triangles have a perimeter of 5 + 4 = 9.
3 triangles have a perimeter of 4 + 5 + 4 + 5 + 5 = 23.
We can now complete the table:
Number of Triangles, x | Perimeter, y | Ordered Pair (xy)
1 | 4 | (1, 4)
2 | 9 | (2, 9)
3 | 23 | (3, 23)
The table shows the relationship between the number of triangles and the corresponding perimeter.
Now let's represent this relationship using words:
The perimeter of the figure formed by 1 triangle is 4.
The perimeter of the figure formed by 2 triangles is 9.
The perimeter of the figure formed by 3 triangles is 23.
For the equation, we can express the relationship as follows:
y = 5x - 1
This equation represents the linear relationship between the number of triangles (x) and the perimeter (y).
Lastly, we can represent this relationship using a graph. On the x-axis, we plot the number of triangles, and on the y-axis, we plot the perimeter. We then connect the plotted points to form a line.