Question

the length of a rectangle is three times its width. the perimeter of the rectangle is a. which inequality models the relationship between the width and the perimeter of the rectangle?

$2w + 2cdot(3w)leq112$

$2w + 2cdot(3w)>112$

$2w + 2cdot(3w)geq112$

$2w + 2cdot(3w)<112$

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2l+2w$, where $l$ is the length and $w$ is the width. Given that $l = 3w$, then $P=2(3w)+2w$.

Step2: Analyze the problem context

We assume the perimeter is at most 112 (since no other information about the comparison direction is given except in the options). So we have $2w + 2(3w)\leq112$.

Answer:

A. $2w + 2\cdot(3w)\leq112$