Answer
$P=6w+2$
Work Step by Step
Since the length is one more than $2$ times the width, $w$, we must multiply $w$ by $2$, and then add $1$ to find the length. This gives us a length of $2w+1$. The formula for the perimeter of a rectangle is $P=2l+2w$, where $l$ is the length and $w$ is the width. We plug in the values for width and length: $P=2(2w+1)+2(w)$
We apply the distributive property to expand the first term: $P=4w+2+2w$
We apply the commutative property of addition to rearrange the things being added: $P=4w+2w+2$
We add to combine like terms: $P=6w+2$
