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: \( P = 2(l + w) \). Our goal is to isolate \( l \). First, we can divide both sides of the equation by 2 to simplify.

$$ \frac{P}{2} = \frac{2(l + w)}{2} $$

Simplifying the right - hand side, the 2 in the numerator and denominator cancels out, so we get:

$$ \frac{P}{2}=l + w $$

Step2: Isolate \( l \)

Now, to get \( l \) by itself, we subtract \( w \) from both sides of the equation \( \frac{P}{2}=l + w \).

$$ \frac{P}{2}-w=l + w - w $$

Since \( w - w = 0 \), the equation simplifies to:

$$ l=\frac{P}{2}-w $$

Answer:

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