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 pentagons
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 exact diagram is not visible to me, as I can only interpret text. However, I can explain the general principle of how to calculate the perimeter of a figure made up of pentagons and then complete a table based on the assumption that the pentagons are arranged in such a way that with each additional pentagon, only one new side is added to the perimeter.
Let's assume each pentagon has all sides equal in length. If we let the length of each side be 's', then the perimeter of one pentagon would be 5s. For each additional pentagon, we would add one side to the perimeter because we assume the pentagons are sharing sides. This would give a general formula of:
Perimeter (y) = (5 + (x - 1)) * s = (4x + 1) * s
The table would then look like this, assuming 's' is some constant unit length:
| Number of Pentagons (x) | Perimeter (y) | Ordered Pair (x,y) |
|--------------------------|---------------|--------------------|
| 1 | 5s | (1, 5s) |
| 2 | 6s | (2, 6s) |
| 3 | 7s | (3, 7s) |
In the above table, for each additional pentagon, we increase the perimeter by 's'.
However, if the diagram has a different configuration, the relationship between x and y may vary. For instance, if each pentagon completely shares a side with the next, the perimeter might increase in different increments. Without the diagram, this is the most generic answer I can provide. If you have more details on how the pentagons are connected, please provide more information, and I can assist you further.