The relationship between the number of pentagons and the perimeter will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
From the diagram in the question, each side of a pentagon has length [tex]3units[/tex].
Also, each time another pentagon is attached, a side is removed.
Using these observations, we can create a relationship between the number of pentagons, [tex]x[/tex], and the perimeter, [tex]y[/tex], as follows
For [tex]x=\text{number of sides}=1[/tex]
[tex]y=\text{perimeter}=3\times 5=15units[/tex]
For [tex]x=2[/tex]
[tex]y=3\times5+3\times5-1\\=15+15-1\\=29units[/tex]
For [tex]x=3[/tex]
[tex]y=3\times5+3\times5-1+3\times5-1\\=3\times5+3\times5+3\times5-1-1\\=15+15+15-2=43units[/tex]
The relationship will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
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