The length of a rectangle is twice the width. The perimeter is 126 centimeters. Which system of equations will determine the length, [tex]L[/tex], and the width, [tex]W[/tex], of the rectangle?

A.
[tex]
\[
\begin{aligned}
L + 2 &= W \\
2L + 2W &= 126
\end{aligned}
\]
[/tex]

B.
[tex]
\[
\begin{aligned}
L + W &= 2 \\
L \cdot W &= 126
\end{aligned}
\]
[/tex]

C.
[tex]
\[
\begin{aligned}
L &= 2W \\
2L + 2W &= 126
\end{aligned}
\]
[/tex]

D.
[tex]
\[
\begin{aligned}
W &= 2L \\
L + 2W &= 126
\end{aligned}
\]
[/tex]

E.
[tex]
\[
\begin{aligned}
2L &= W \\
L + W &= 126
\end{aligned}
\]
[/tex]

To solve this question about finding the system of equations that represents the rectangle's dimensions, follow these steps:

1. Understand the Problem Statement:
- We are told that the length of the rectangle (L) is twice the width (W). This gives us the first equation:
[tex]$ L = 2W $[/tex].

2. Perimeter Information:
- The perimeter of a rectangle is given by the formula:
[tex]$ \text{Perimeter} = 2L + 2W $[/tex].
- We know the perimeter is 126 centimeters. So, we have the second equation:
[tex]$ 2L + 2W = 126 $[/tex].

3. Formulate the System of Equations:
- From the information given, we can write the system of equations as follows:
1. [tex]$ L = 2W $[/tex]
2. [tex]$ 2L + 2W = 126 $[/tex]

These equations can help us solve for both [tex]$ L $[/tex] and [tex]$ W $[/tex] where [tex]$ L $[/tex] is the length and [tex]$ W $[/tex] is the width of the rectangle. Therefore, the correct choice of system of equations is Option C:
- [tex]$ L = 2W $[/tex]
- [tex]$ 2L + 2W = 126 $[/tex]

These equations accurately represent the relationship between the length, width, and perimeter given in the problem.