Question

the length of a rectangle is four times its width. the perimeter of the rectangle is at most 130 cm. which inequality models the relationship between the width and the perimeter of the rectangle? 2w + 2·(4w) ≤ 130 2w + 2·(4w) ≥ 130 2w + 2·(4w) > 130 2w + 2·(4w) < 130

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

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

Step2: Substitute the given relationship between length and width

Given that \(l = 4w\). Substituting \(l = 4w\) into the perimeter formula, we get \(P=2(4w)+2w\).

Step3: Interpret the phrase "at most"

The phrase "at most" means less than or equal to. If the perimeter \(P\) is at most \(130\) cm, then \(2(4w)+2w\leq130\).

Answer:

\(2w + 2\cdot(4w)\leq130\) (the first option)