Question

the length of a rectangle is three times its width. the perimeter of the rectangle is at most 112 cm. which inequality models the relationship between the width and the perimeter of the rectangle? 2w + 2·(3w) ≤ 112 2w + 2·(3w) < 112 2w + 2·(3w) > 112 2w + 2·(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.

Step2: Substitute length - width relationship

Given that $l = 3w$, substitute $l$ into the perimeter formula: $P=2(3w)+2w$.

Step3: Apply perimeter condition

The perimeter is at most 112 cm, which means $P\leq112$. So, $2(3w)+2w\leq112$.

Answer:

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