Question

the formula for the perimeter of a rectangle is $p = 2l + 2w$, where $p$ is the perimeter, $l$ is the length, and $w$ is the width. rearrange the formula to find a formula for the width of the rectangle if you know the perimeter and the length.
a $w=\frac{2l - p}{2}$
b $w=\frac{p - 2l}{2}$
c $w = p - 2l$
d $w=\frac{l - p}{2}$

Explanation:

Step1: Start with the formula \( P = 2l + 2w \)

We need to solve for \( w \) in terms of \( P \) and \( l \).

Step2: Subtract \( 2l \) from both sides

\( P - 2l = 2w \)

Step3: Divide both sides by 2

\( w=\frac{P - 2l}{2}\) (which can also be written as \( w=\frac{P}{2}-l \) or \( w=\frac{P - 2l}{2}\), and looking at the options, option B is \( w=\frac{P - 2l}{2}\) (assuming the option B was written with a typo and should be \( w=\frac{P - 2l}{2}\) as the correct rearrangement))

Answer:

B. \( w=\frac{P - 2l}{2} \)