Answer:
[tex]140[/tex]
Step-by-step explanation:
A regular polygon is a shape with equal sides and angles. Because of this, we can write the following equation to set two sides equal to each other:
[tex]3a+b+3=2a+2b+6[/tex]
Solving, we will get a in terms of b:
[tex]3a=2a+b+3,\\a=b+3[/tex]
Now we can substitute a for (b+3) into our equation:
[tex]5a-2b+1=2a+2b+6,\\5(b+3)-2b+1=2(b+3)+2b+6,\\3b+16=4b+12,\\-b=-4,\\b=\boxed{4}[/tex]
Therefore, the length of each side of this polygon is [tex]5(4+3)-2(4)+1=28[/tex].
Since the perimeter of the polygon consists of all five sides, the perimeter is:
[tex]p=28\cdot 5 =\boxed{140}[/tex]
