Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]L + 2 = W[/tex]
[tex]2L + 2W = 126[/tex]

B. [tex]L + W = 2[/tex]

C. [tex]L = 2W[/tex]
[tex]2L + 2W = 126[/tex]

D. [tex]W = 2L[/tex]
[tex]L + 2W = 126[/tex]

E. [tex]2L = W[/tex]
[tex]L + W = 126[/tex]

To solve this problem, we need to formulate a system of equations based on the information provided about the rectangle.

1. Understand the problem:
- You have a rectangle with a length (L) and a width (W).
- The length is twice the width.
- The perimeter of the rectangle is 126 centimeters.

2. Translate the information into equations:
- Since the length is twice the width, we can express this relationship as:
[tex]\[
L = 2W
\][/tex]
- The formula for the perimeter [tex]$ P $[/tex] of a rectangle is:
[tex]\[
P = 2L + 2W
\][/tex]
We know the perimeter is 126 centimeters, so:
[tex]\[
2L + 2W = 126
\][/tex]

3. Form the system of equations:
Combining the two equations we derived:
[tex]\[
\begin{align*}
L &= 2W \\
2L + 2W &= 126
\end{align*}
\][/tex]

4. Identify the correct option:
- Looking at the options, we search for the system of equations that matches:
- [tex]$ L = 2W $[/tex]
- [tex]$ 2L + 2W = 126 $[/tex]

The correct option is:
- Option C:
[tex]\[
\begin{align*}
L &= 2W \\
2L + 2W &= 126
\end{align*}
\][/tex]

Therefore, the correct system of equations is given in option C.