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 13 (1,13)
2 18 (2,18)
3 22 (3,23)
(Simplify your answers)
Represent the relationship using words.
Multiply the number of triangles in each figure by __ to get the total length of the ___ (top and bottom or left and right) sides of the combined figure. Then add __ for the total length the of the ___ (top and bottom or left and right) sides of the combined figure to get the entire perimeter .
Multiply the number of triangles in each figure by 4 to get the total length of the top and bottom sides of the combined figure. Then add 5 for the total length of the left and right sides of the combined figure to get the entire perimeter.
Represent the relationship using an equation.
Let x represent the number of triangles.
The equation relating x and y (perimeter) can be expressed as:
y = 4x + (x-1)
Represent the relationship using a graph.
The graph will have x (number of triangles) on the x-axis and y (perimeter) on the y-axis.
Each ordered pair (x, y) from the table can be plotted on the graph.
The graph will show a linear relationship where the y values increase as the x values increase.
To represent the relationship between the number of triangles and the perimeter using words, we can describe the pattern observed in the diagram.
To find the perimeter of the figure formed by the triangles, we can follow these steps:
1. Multiply the number of triangles in each figure by 4. This is because each triangle has 3 sides, and we need to account for both the top/bottom and left/right sides of the figure. As each side of a triangle is counted twice in the perimeter calculation, we multiply the number of triangles by 4.
2. Add the result from step 1 to the length of the top/bottom or left/right sides of the combined figure. The combined figure consists of consecutive sides shared by the triangles. In the given pattern, each additional triangle introduces one more side to the combined figure.
Let me fill in the missing details in the word representation:
Multiply the number of triangles in each figure by 4 to get the total length of the top/bottom or left/right sides of the combined figure. Then add the length of the top/bottom or left/right sides of the combined figure to get the entire perimeter.