Question

the formula for the perimeter of a rectangle is $p = 2l + 2w$, where $l$ is the length and $w$ is the width. a given rectangle has a perimeter of 42 feet and a length that is 7 feet greater than its width. write the equation which represents the perimeter of the rectangle.

$42 = 2(l + 7) + 2w$

$42 = 2l + 2(w + 7)$

$42 = 2l + 2(l + 7)$

$42 = 2(w + 7) + 2w$

Explanation:

Step1: Express length in terms of width

Given that length \(l\) is 7 feet greater than width \(w\), so \(l = w + 7\)

Step2: Substitute \(l = w + 7\) into perimeter formula \(P=2l + 2w\)

Substitute \(l\) in \(P = 2l+2w\), we get \(P=2(w + 7)+2w\). Since \(P = 42\), the equation is \(42=2(w + 7)+2w\)

Answer:

\(42 = 2(w + 7)+2w\) (the fourth option in the given list)