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 tangles. Let ythe perimeter of the figure.
1 triangle 3 3 4 2 triangle 4 3 3 4 3 triangle 4 3 3 4 4
Represent the relationship using a table. Complete the table below.
Number of Triangles, x 1 2 3
Perimeter y _ _
Ordered (x,y) _ _
(Simplify your answers.)
Number of Triangles, x 1 2 3
Perimeter y 3 10 17
Ordered (x,y) (1,3) (2,10) (3,17)
Number of Triangles, x 1 2 3
Perimeter y 4 10 16
Ordered (x,y) (1,4) (2,10) (3,16)
To determine the relationship between the number of triangles and the perimeter of the figure they form, we can analyze the given data and complete the table.
Based on the given data, we have:
1 triangle: Perimeter = 3
2 triangles: Perimeter = 3 + 4 = 7
3 triangles: Perimeter = 3 + 4 + 3 + 4 = 14
Using this information, we can complete the table:
Number of Triangles, x 1 2 3
Perimeter, y 3 7 14
Ordered (x,y) (1, 3) (2, 7) (3, 14)
Now let's represent this relationship using words, an equation, and a graph:
- Words: The perimeter of the figure formed by a certain number of triangles can be determined by multiplying the number of triangles by 7, since each additional triangle contributes a perimeter of 7 units.
- Equation: y = 7x
- Graph:
|
15 |
| . (3,14)
10 | .
| .
5 | .
| .
0 | (0,0) .
|_____________
0 1 2 3 4
Note: The graph assumes the x-axis represents the number of triangles (x) and the y-axis represents the perimeter (y). The dots represent the corresponding data points from the table. The line connecting the dots represents the linear relationship between the number of triangles and the perimeter.