Question

the width of a rectangle measures (9v - 5w) centimeters, and its length measures (9v + 6w) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
1 + 18v
2 + 36v
36v + 2w
-5 + 12w + 36v

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=(9v + 6w)$ and $w=(9v - 5w)$.

Step2: Substitute length and width

$P=2((9v + 6w)+(9v - 5w))$.

Step3: Simplify inside parentheses

$(9v + 6w)+(9v - 5w)=9v+9v + 6w-5w=18v + w$.

Step4: Multiply by 2

$P = 2(18v+w)=36v + 2w$.

Answer:

$36v + 2w$ (corresponding to the option "36v + 2w")