To determine which equation is equivalent to the given equation for the perimeter of a rectangle, let's start with Paolo's equation:
[tex]\[ P = 2(l + w) \][/tex]
Our goal is to isolate [tex]\( w \)[/tex] on one side of the equation. Follow these steps:
1. Divide both sides by 2 to begin isolating [tex]\( w \)[/tex]:
[tex]\[ \frac{P}{2} = l + w \][/tex]
2. Subtract [tex]\( l \)[/tex] from both sides to solve for [tex]\( w \)[/tex]:
[tex]\[ w = \frac{P}{2} - l \][/tex]
This simplified equation matches one of the given choices. Therefore, the equation equivalent to Paolo's equation is:
[tex]\[ w = \frac{P - 2l}{2} \][/tex]
