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 attempt 1 out of 2 -14 + 16r 16r - 14s -7 + 8r -2 - 10s + 16r

Explanation:

Step1: Recall perimeter formula

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

Step2: Substitute values into formula

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

Step3: Simplify inside the parentheses

First, combine like - terms inside the parentheses: $(r+7r)+(- 5s-2s)=8r - 7s$. So $P = 2(8r - 7s)$.

Step4: Distribute the 2

Using the distributive property $a(b + c)=ab+ac$, we have $P=2\times8r-2\times7s = 16r-14s$.

Answer:

$16r - 14s$