1. The length of a rectangle is twice its width. The perimeter of the rectangle is 24 inches. Write a system of equations in 2 variables. Use substitution to solve the problem.
A. Equation 1: L = 2W
L= 2(4) = 8
Equation 2: 2L + 2W = 24
2(2W) + 2W = 24
6W = 24
W = 24/6 = 4
(i would like help checking the Equations)
The answer is 16
Let's go through the equations and check them together.
Equation 1: L = 2W
In this equation, L represents the length of the rectangle, and W represents its width. Since it is given that "The length of a rectangle is twice its width," the equation L = 2W is correct.
Now, let's solve Equation 1 using the given value.
L = 2(4)
L = 8
So, the length of the rectangle is indeed 8.
Now, let's move on to Equation 2: 2L + 2W = 24
In this equation, 2L represents the sum of the two lengths of the rectangle (since there are two lengths in a rectangle) and 2W represents the sum of the two widths (again, two widths in a rectangle). It is given that "The perimeter of the rectangle is 24 inches," so the equation 2L + 2W = 24 is correct.
Now let's solve Equation 2:
2(8) + 2W = 24
16 + 2W = 24
2W = 24 - 16
2W = 8
W = 8 / 2
W = 4
So, the width of the rectangle is indeed 4.
Both equations are correctly set up, and when solved, they give the values of length (L = 8) and width (W = 4), which satisfy the given conditions.
To check if the equations are correct, let's substitute the value of W = 4 into Equation 1 and Equation 2:
Equation 1: L = 2W
L = 2 * 4
L = 8
Equation 2: 2L + 2W = 24
2(8) + 2(4) = 24
16 + 8 = 24
24 = 24
Both equations hold true when W = 4 and L = 8. Thus, the equations are correct.
Now let's proceed with solving the system of equations using substitution:
Equation 1: L = 2W
Substitute the value of L from Equation 1 into Equation 2:
2L + 2W = 24
2(2W) + 2W = 24
4W + 2W = 24
6W = 24
W = 24/6
W = 4
Now substitute the value of W = 4 into Equation 1 to find L:
L = 2W
L = 2 * 4
L = 8
Therefore, the width of the rectangle is 4 inches and the length is 8 inches.
ERquation 1.
L = 2 W
2 W = L
Equation 2.
2 W + 2 L = 24
Substitution: 2 W = L
L + 2 L = 24
3 L = 24
L = 24 / 3 = 8 in
L = 2 W
8 = 2 W
8 / 2 = W
W = 4 in