Question

1. choose efficient methods the formula for the perimeter of a rectangle is $2ell + 2w$, where $ell$ is the length and $w$ is the width. how can you use the distributive property to write an equivalent expression for $2ell + 2w$?

Explanation:

Step1: Recall the Distributive Property

The Distributive Property states that \(a(b + c)=ab+ac\). In reverse, \(ab + ac=a(b + c)\).

Step2: Apply the Distributive Property to \(2\ell+2w\)

Here, \(a = 2\), \(b=\ell\), and \(c = w\). Using the reverse of the Distributive Property \(ab+ac=a(b + c)\), we substitute the values: \(2\ell+2w=2(\ell + w)\)

Answer:

\(2(\ell + w)\)