Answer :
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.
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.