Question

question: the width of a rectangle measures (7r - 2s) centimeters, and its length measures (r - 5s) centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer: - 14 + 16r, - 7 + 8r, 16r - 14s, - 2 - 10s + 16r

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=(r - 5s)$ and $w=(7r-2s)$.

Step2: Substitute length and width into formula

$P = 2((r - 5s)+(7r - 2s))$.

Step3: Simplify the expression inside the parentheses

$(r - 5s)+(7r - 2s)=r+7r-5s - 2s=8r-7s$.

Step4: Multiply by 2

$P = 2(8r-7s)=16r-14s$.

Answer:

$16r - 14s$