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Makayta is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for [tex]W[/tex], where [tex]P[/tex] is the perimeter, [tex]L[/tex] is the length, and [tex]W[/tex] is the width of the rectangle:

[tex]\[ P = 2L + 2W \][/tex]

A. [tex]W = 2P - 2[/tex]
B. [tex]W = \frac{F}{2} - 2L[/tex]
C. [tex]W = \frac{P - 2L}{2}[/tex]
D. [tex]W = 2P + 2L[/tex]

Sagot :

GinnyAnswer
Certainly! Let's start with the equation for the perimeter of a rectangle:

[tex]\[ P = 2L + 2W \][/tex]

where \( P \) is the perimeter, \( L \) is the length, and \( W \) is the width. Our goal is to solve for \( W \). Here's a step-by-step process to isolate \( W \):

1. Start with the perimeter equation:
[tex]\[ P = 2L + 2W \][/tex]

2. Subtract \( 2L \) from both sides of the equation to start isolating \( W \):
[tex]\[ P - 2L = 2W \][/tex]

3. Now, divide both sides of the equation by 2 to solve for \( W \):
[tex]\[ W = \frac{P - 2L}{2} \][/tex]

So, the solution to the given equation is:

[tex]\[ W = \frac{P - 2L}{2} \][/tex]

Looking at the given options, we see that:

[tex]\[ W = \frac{P - 2L}{2} \][/tex]

matches our derived solution. This is the correct rearrangement of the equation to solve for [tex]\( W \)[/tex].
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