Let $P$ be a convex polygon with sides $5, 4, 4, 3$. For example, the following:
Consider the shape in the plane that consists of all points within distance $1$ from some point in $P$. If $\ell$ is the perimeter of the shape, which of the following is always correct?
- $\ell$ cannot be determined from the given information.
- $20\leq \ell < 21$
- $21\leq \ell< 22$
- $22\leq \ell< 23$
- $23\leq \ell< 24$
