Question

rectangles the formula ( p = 2ell + 2w ) represents the perimeter of a rectangle. in this formula, ( ell ) is the length of the rectangle and ( w ) is the width. solve the formula for ( ell ).

Explanation:

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

We start with the formula for the perimeter of a rectangle: \(P = 2\ell+ 2w\). To isolate the term with \(\ell\), we subtract \(2w\) from both sides of the equation. This gives us \(P - 2w=2\ell + 2w- 2w\), which simplifies to \(P - 2w = 2\ell\).

Step2: Divide both sides by 2

Now that we have \(P - 2w = 2\ell\), we want to solve for \(\ell\). We divide both sides of the equation by 2. So, \(\frac{P - 2w}{2}=\frac{2\ell}{2}\), which simplifies to \(\ell=\frac{P - 2w}{2}\) (or we can also write it as \(\ell=\frac{P}{2}-w\) by splitting the fraction).

Answer:

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