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) _ _
Number of Triangles, x 1 2 3
Perimeter y 3 6 9
Ordered (x,y) (1,3) (2,6) (3,9)
Number of Triangles, x 1 2 3
Perimeter y _ _ _
Ordered (x,y) _ _
To complete the table, we need to determine the perimeter for each number of triangles.
Number of Triangles, x 1 2 3
Perimeter y 3 _ _
Ordered (x,y) _ _
From the given information in the diagram, we can see that when there is 1 triangle, the perimeter is 3.
Number of Triangles, x 1 2 3
Perimeter y 3 _ _
Ordered (x,y) _ _
For the case of 2 triangles, the perimeter is also 3.
Number of Triangles, x 1 2 3
Perimeter y 3 3 _
Ordered (x,y) _ _
For the case of 3 triangles, the perimeter is 4.
Number of Triangles, x 1 2 3
Perimeter y 3 3 4
Ordered (x,y) _ _
The completed table is:
Number of Triangles, x 1 2 3
Perimeter y 3 3 4
Ordered (x,y) _ _
To determine the relationship between the number of triangles and the perimeter of the figure they form, we need to analyze the given diagram.
Looking at the diagram, we can see that each additional triangle contributes certain sides to the perimeter of the figure. From the given information, we can determine the following patterns:
For 1 triangle: Perimeter = 3
For 2 triangles: Perimeter = 3 + 4 = 7
For 3 triangles: Perimeter = 3 + 4 + 4 = 11
Now, let's complete the table using the determined information:
Number of Triangles, x 1 2 3
Perimeter, y 3 7 11
Ordered (x,y) (1,3) (2,7) (3,11)
So, the completed table is as follows:
Number of Triangles, x 1 2 3
Perimeter, y 3 7 11
Ordered (x,y) (1,3) (2,7) (3,11)
This table represents the relationship between the number of triangles (x) and the perimeter of the figure (y).
To represent this relationship through words, we can say that the perimeter of the figure increases by 4 units each time a new triangle is added.
For the equation, we can express the relationship as follows:
y = 4x - 1
Lastly, let's create a graph to visualize the relationship between the number of triangles and the perimeter:
[Graph]