In the diagram below, what is the relationship between the number of and the perimeter of the figure they form? Represent this relationship using a table, words, an equation, and a graph. Let xthe number of . Let ythe perimeter of the figure.
3
3
3
3
1 pentagon
2 pentagons
3 pentagons
3
Question content area bottom
Part 1
Represent the relationship using a table. Complete the table below.
Number of , x
Perimeter, y
Ordered Pair (x,y)
1
enter your response here
enter your response here
2
enter your response here
enter your response here
3
enter your response here
enter your response here
(Simplify your answers.)
Number of x, Number of Pentagons
Perimeter, y
Ordered Pair (x,y)
1 15 (1, 15)
2 30 (2, 30)
3 45 (3, 45)
Question content area top
Part 1
In the diagram below, what is the relationship between the number of and the perimeter of the figure they form? Represent this relationship using a table, words, an equation, and a graph. Let xthe number of . Let ythe perimeter of the figure.
3
3
3
3
1 pentagon
2 pentagons
3 pentagons
3
Question content area bottom
Part 1
Represent the relationship using a table. Complete the table below.
Number of , x
Perimeter, y
Ordered Pair (x,y)
1
15
left parenthesis 1 comma 15 right parenthesis
2
24
left parenthesis 2 comma 24 right parenthesis
3
33
left parenthesis 3 comma 33 right parenthesis
(Simplify your answers.)
Part 2
Represent the relationship using words.
Multiply the number of in each figure by
enter your response here,
▼
sides the combined figure. Then add
enter your response here for
▼
two
three
the combined figure to get the entire perimeter.
Part 2
Represent the relationship using words.
Multiply the number of pentagons in each figure by 5 (since a pentagon has 5 sides) to get the perimeter of the combined figure. Then add 15 (the perimeter of one pentagon) for each pentagon in the combined figure to get the entire perimeter.
To determine the relationship between the number of pentagons (x) and the perimeter of the figure they form (y), we can observe the pattern and fill in the table.
Number of pentagons (x) - Perimeter, y - Ordered Pair (x,y)
1 - 5s - (1,5s)
2 - 10s - (2,10s)
3 - 15s - (3,15s)
In this case, the perimeter of the figure is directly proportional to the number of pentagons. Each pentagon adds 5s to the perimeter, where s represents the side length of the pentagon.
Therefore, the equation representing this relationship is: y = 5sx
To represent this relationship using a graph, you can plot the ordered pairs (x,y) for different values of x and y. The x-axis would represent the number of pentagons (x), and the y-axis would represent the perimeter (y). Then you can connect the data points to form a straight line, which represents the linear relationship between the variables.