To solve for the length [tex]\( l \)[/tex] in the given perimeter formula for a rectangle, [tex]\( P = 2w + 2l \)[/tex], we need to rearrange the equation step-by-step:
1. Starting Equation:
[tex]\[ P = 2w + 2l \][/tex]
2. Isolate the term involving [tex]\( l \)[/tex]:
Subtract [tex]\( 2w \)[/tex] from both sides of the equation:
[tex]\[ P - 2w = 2l \][/tex]
3. Solve for [tex]\( l \)[/tex]:
Divide both sides of the equation by 2:
[tex]\[ l = \frac{P - 2w}{2} \][/tex]
4. Simplify the Expression:
Distribute the division:
[tex]\[ l = \frac{P}{2} - \frac{2w}{2} \][/tex]
[tex]\[ l = \frac{P}{2} - w \][/tex]
Therefore, the correctly rearranged formula for the length [tex]\( l \)[/tex] is:
[tex]\[ l = \frac{P}{2} - w \][/tex]
Among the given options:
- [tex]\( l = P - \frac{1}{2}w \)[/tex]
- [tex]\( l = \frac{1}{2}w - P \)[/tex]
- [tex]\( l = 2P - 2w \)[/tex]
- [tex]\( l = \frac{1}{2}P - w \)[/tex]
The correct answer is:
[tex]\[ l = \frac{1}{2}P - w \][/tex]
