Question

the formula for the perimeter of a rectangle is:
$p = 2(l + w)$
where:

• $p$ = perimeter
• $l$ = length
• $w$ = width

which equation correctly isolates $l$?

• $l = \frac{p}{2} - w$
• $l = \frac{p - w}{2}$
• $l = \frac{p}{2w}$
• $l = p - 2w$

Explanation:

Step1: Start with the perimeter formula

We have the formula for the perimeter of a rectangle: \( P = 2(l + w) \).

Step2: Divide both sides by 2

To isolate the term with \( l \), we divide both sides of the equation by 2. This gives us \( \frac{P}{2}=l + w \).

Step3: Subtract \( w \) from both sides

Now, to solve for \( l \), we subtract \( w \) from both sides of the equation \( \frac{P}{2}=l + w \). This results in \( l=\frac{P}{2}-w \).

Answer:

\( l = \frac{P}{2} - w \) (the first option)