Question

the width of a rectangle measures (5v - w) centimeters, and its length measures (6v + 8w) centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer 7 + 11v 14 + 22v 22v + 16w - 1 14w + 22v

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width.

Step2: Substitute given length and width

Here, $l=(6v + 8w)$ and $w=(5v - w)$. So $P = 2((6v + 8w)+(5v - w))$.

Step3: Simplify inside the parentheses

$(6v + 8w)+(5v - w)=6v+5v + 8w - w=11v + 7w$.

Step4: Multiply by 2

$P = 2(11v + 7w)=22v+14w$.

Answer:

$14w + 22v$