Question

the formula for the perimeter of a rectangle is $p = 2l + 2w$. solve the formula for $l$ in terms of $p$ and $w$.

Explanation:

Step1: Subtract \(2w\) from both sides

To isolate the term with \(l\), we subtract \(2w\) from both sides of the equation \(P = 2l + 2w\). This gives us \(P - 2w = 2l + 2w - 2w\), which simplifies to \(P - 2w = 2l\).

Step2: Divide both sides by 2

To solve for \(l\), we divide both sides of the equation \(P - 2w = 2l\) by 2. So we have \(\frac{P - 2w}{2}=l\), which can also be written as \(l=\frac{P - 2w}{2}\) or \(l=\frac{P}{2}-w\).

Answer:

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