The length of a rectangle is five times its width. The perimeter of the rectangle is at most 96 cm.

Question

Which inequality models the relationship between the width and the perimeter of the rectangle?



Responses

12w≤96
2 w plus 2 times left parenthesis 5 w right parenthesis less than or equal to 96

12w<96
2 w plus 2 times left parenthesis 5 w right parenthesis less than 96

12w≥96
2 w plus 2 times left parenthesis 5 w right parenthesis greater than or equal to 96

12w>96

Answer 1

To model the relationship between the width and the perimeter of the rectangle, let's denote the width of the rectangle as \( w \).

Given that the length \( l \) is five times the width, we have: \[ l = 5w \]

The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2l + 2w \]

Substituting the expression for the length into the perimeter formula, we get: \[ P = 2(5w) + 2w = 10w + 2w = 12w \]

According to the problem, the perimeter is at most 96 cm, which can be expressed as: \[ 12w \leq 96 \]

Therefore, the correct inequality that models the relationship between the width and the perimeter of the rectangle is: 12w ≤ 96.