Question

the length of a rectangle is 4 feet less than 3 times its width. the perimeter of the rectangle is 54 feet. what equation can be used to find the width (w) of the rectangle?
a. (3w - 4) + 2w = 54
b. 2(3w - 4) + 2w = 54
c. w(3w - 4) = 54
d. 2(4w - 3) + 2w = 54

Explanation:

Step1: Recall the perimeter formula

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

Step2: Express the length in terms of width

Given that the length \(l=3w - 4\) and \(P = 54\).

Step3: Substitute into the perimeter formula

Substitute \(l = 3w-4\) and \(P = 54\) into \(P = 2(l + w)\). We get \(54=2((3w - 4)+w)\).

Answer:

B. \(2(3w - 4)+2w = 54\)