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 ___ sides of the combined figure. Then add __ for the total length the of the ___ 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 equal sides of the combined figure. Then add 5 for the total length of the unequal sides of the combined figure to get the entire perimeter.
Multiply the number of triangles in each figure by 5 to get the total length of the 4 sides of the combined figure. Then add 3 for the total length of the 3 sides of the combined figure to get the entire perimeter.
The relationship between the number of triangles and the perimeter of the figure they form can be represented using a table, words, an equation, and a graph.
To complete the table, we need to find the perimeter of each figure for different numbers of triangles.
For the given figures:
- 1 triangle: The perimeter is 4 + 4 + 5 = 13
- 2 triangles: The perimeter is 5 + 4 + 5 + 4 = 18
- 3 triangles: The perimeter is 4 + 5 + 4 + 5 + 5 = 23
Now we can complete the table:
Number of Triangles (x) | Perimeter (y) | Ordered Pair (xy)
-------------------------------------------------------------
1 | 13 | (1, 13)
2 | 18 | (2, 18)
3 | 23 | (3, 23)
Now, let's represent the relationship using words.
To find the perimeter of the figure formed by multiple triangles, we need to follow these steps:
1. Multiply the number of triangles in each figure by the total length of their shared sides.
For example, for 1 triangle, we have 1 x (4 + 4 + 5) = 13.
2. Add the total length of the individual sides of all the triangles to the result from step 1.
For example, for 1 triangle, we have 13 + 0 = 13 (as there are no other sides).
3. This sum gives us the perimeter of the combined figure.
Finally, let's represent the relationship using an equation and a graph.
Equation: y = mx + b
In this case, the equation would be y = x + 12.
Graph:
The graph would show the relationship between the number of triangles (x) and the perimeter (y) on a coordinate plane, where x is plotted on the x-axis and y is plotted on the y-axis. The points (1, 13), (2, 18), and (3, 23) would be plotted, showing a linear relationship between the number of triangles and the perimeter.