Question

Please help and thank you

Answer 1

A.
`11(5)/(8)\textrm{ inches}`

Explanation:

Given:

The regular polygon is a decagon having 10 sides.

Perimeter of the given polygon is,

`P=116(1)/(4)\textrm{ inches}=116.25\textrm{ inches}`.

We know that, perimeter of a regular polygon of
`n` sides is given as,

`P=na` where,
`a` is the length of each side.

Here,
`n=10,P=116(1)/(4)\textrm{ in}`

Plug in these values and solve for
`a`. This gives,

`P=na\\116(1)/(4)=10a\\116.25=10a\\a=(116.25)/(10)=11.625=11+(625)/(1000)=11+(5)/(8)=11(5)/(8)\textrm{ in}`

Therefore, the side length of the given polygon is
`11(5)/(8)\textrm{ inches}`