Answer:
A. [tex]11\frac{5}{8}\textrm{ inches}[/tex]
Step-by-step explanation:
Given:
The regular polygon is a decagon having 10 sides.
Perimeter of the given polygon is,
[tex]P=116\frac{1}{4}\textrm{ inches}=116.25\textrm{ inches}[/tex].
We know that, perimeter of a regular polygon of [tex]n[/tex] sides is given as,
[tex]P=na[/tex] where, [tex]a[/tex] is the length of each side.
Here, [tex]n=10,P=116\frac{1}{4}\textrm{ in}[/tex]
Plug in these values and solve for [tex]a[/tex]. This gives,
[tex]P=na\\116\frac{1}{4}=10a\\116.25=10a\\a=\frac{116.25}{10}=11.625=11+\frac{625}{1000}=11+\frac{5}{8}=11\frac{5}{8}\textrm{ in}[/tex]
Therefore, the side length of the given polygon is [tex]11\frac{5}{8}\textrm{ inches}[/tex]
