Let's work through the given perimeter equation and find an equivalent equation for width [tex]\( w \)[/tex].
1. Start with the given perimeter equation:
[tex]\[
P = 2(l + w)
\][/tex]
2. Isolate [tex]\( l + w \)[/tex] by dividing both sides of the equation by 2:
[tex]\[
\frac{P}{2} = l + w
\][/tex]
3. Isolate [tex]\( w \)[/tex] by subtracting [tex]\( l \)[/tex] from both sides:
[tex]\[
\frac{P}{2} - l = w
\][/tex]
4. Rewriting this equation gives us:
[tex]\[
w = \frac{P}{2} - l
\][/tex]
This can also be rewritten as:
[tex]\[
w = \frac{P - 2l}{2}
\][/tex]
Among the given choices, the equivalent equation is:
[tex]\[
w = \frac{P - 2l}{2}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{w=\frac{P-2 l}{2}}
\][/tex]
