In the diagram below, what is the relationship between the number of pentagons
and the perimeter of the figure they form? Represent this relationship using a table, words, an equation, and a graph. Let xequals
the
number of pentagons
.
Let yequals
the
perimeter of the figure.
22221 pentagon2 pentagons3 pentagons2
Question content area bottom
Part 1
Represent the relationship using a table. Complete the table below.
Number of Pentagons
,
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.)
Unfortunately, the diagram you are referring to is not visible in this text format. However, I can still provide you with a general way to determine the relationship between the number of pentagons and the perimeter of the figure they form, and then we can create a hypothetical example if needed.
Assuming that the pentagons are regular (all sides are of equal length) and they are arranged in such a way that each pentagon shares one side with another (except the first and last if arranged in a line), we can follow this reasoning:
- Each pentagon has 5 sides.
- When two pentagons are placed next to each other, they share a side, so the total number of sides is not simply multiplied by the number of pentagons.
- If we add one pentagon to another, we are only adding 4 new sides to the perimeter because one side is shared.
Let's denote the length of each side of a pentagon as `s`.
For one pentagon:
- The perimeter `y` would be 5 times the length of a side `s`.
For two pentagons:
- Since they share a side, we only add four sides to the perimeter, which would be 5s + 4s.
For three pentagons:
- Yet again, when adding the third pentagon, we only add another four sides, making it 5s + 4s + 4s.
So, to write an equation for `y` perimeter for `x` pentagons:
y = 5s + 4s(x - 1)
Now, let's suppose the length of one side `s` is a fixed constant (for example, 1 unit to simplify), and use that to fill out the table:
Number of Pentagons, x | Perimeter, y | Ordered Pair (x, y)
1 | 5 | (1, 5)
2 | 9 | (2, 9)
3 | 13 | (3, 13)
So the equation would be simplified as:
y = 5 + 4(x - 1)
To represent the relationship using a graph, you would simply plot the ordered pairs on a coordinate plane with `x` on the horizontal axis and `y` on the vertical axis, and draw a line through the points. The graph would show a linear relationship starting from the point (1, 5) and going up by 4 units for each additional pentagon.