Sure, let’s solve this step by step.
We are given the formula for the perimeter [tex]\( p \)[/tex] of a rectangle, which is:
[tex]\[ p = 2l + 2w \][/tex]
We need to rewrite this formula to solve for width [tex]\( w \)[/tex].
### Step-by-Step Solution:
1. Original Formula:
[tex]\[ p = 2l + 2w \][/tex]
2. Isolate the Term Involving [tex]\( w \)[/tex]:
We want to get [tex]\( w \)[/tex] by itself on one side of the equation. First, subtract [tex]\( 2l \)[/tex] from both sides:
[tex]\[ p - 2l = 2w \][/tex]
3. Solve for [tex]\( w \)[/tex]:
Next, to solve for [tex]\( w \)[/tex], divide both sides of the equation by 2:
[tex]\[ w = \frac{p - 2l}{2} \][/tex]
So, the formula for [tex]\( w \)[/tex] in terms of [tex]\( p \)[/tex] and [tex]\( l \)[/tex] is:
[tex]\[ w = \frac{p - 2l}{2} \][/tex]
This is the simplified formula to determine the width [tex]\( w \)[/tex] if you know the perimeter [tex]\( p \)[/tex] and the length [tex]\( l \)[/tex] of the rectangle.
Let's compare the solutions provided in the options:
1. [tex]\( w = \frac{p + 2l}{2} \)[/tex] [tex]\( \quad \text{(Incorrect)} \)[/tex]
2. [tex]\( w = \frac{p - 2t}{2} \)[/tex] [tex]\( \quad \text{(Incorrect if \( t \)[/tex] is a typo and should be [tex]\( l \)[/tex])} \)
3. [tex]\( w = 2(p - 2l) \)[/tex] [tex]\( \quad \text{(Incorrect)} \)[/tex]
4. [tex]\( w = 2(2l - p) \)[/tex] [tex]\( \quad \text{(Incorrect)} \)[/tex]
The correct answer is:
[tex]\[ w = \frac{p - 2l}{2} \][/tex]
Thus, none of the provided options are correct except for a potential typo with "t" in option two. The correct rewritten formula for this question should be:
[tex]\[ w = \frac{p - 2l}{2} \][/tex]
