Question

12 a rectangle has a length of 3 times its width. if the perimeter is 48 inches, which equation represents this situation?
a ( 2w + 2l = 24 )
b ( 2w + 2(3w) = 48 )
c ( 2w + 2(3l) = 48 )
d ( 2w + 2l = 48 )

Explanation:

Step1: Recall the perimeter formula of a rectangle

The perimeter formula of a rectangle is \(P = 2w+2l\), where \(w\) is the width and \(l\) is the length. Given that \(P = 48\), so \(2w + 2l=48\).

Step2: Express the length in terms of the width

Since the length \(l\) is 3 times the width \(w\), then \(l = 3w\).

Step3: Substitute \(l = 3w\) into the perimeter formula

Substitute \(l = 3w\) into \(2w + 2l=48\), we get \(2w+2(3w)=48\).

Answer:

B. \(2w + 2(3w)=48\)