The perimeter of a rectangular cattle enclosure is 400 feet. It is 40 feet longer than it is wide. Using a system of equations solve for the length and width of the enclosure using the substitution method.
2 L + 2 w = 400
L + w = 200
L = w + 40
so
w + 40 + w = 200
To solve this problem using the substitution method, we need to set up a system of equations based on the given information.
Let's denote the width of the enclosure as 'w' and the length as 'l'. We can create the following equations:
1. The perimeter of a rectangle is given by the formula: perimeter = 2(length + width)
We are given that the perimeter of the cattle enclosure is 400 feet:
400 = 2(l + w) (Equation 1)
2. It is given that the length of the enclosure is 40 feet longer than its width:
l = w + 40 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2). We can use the substitution method to solve it by substituting Equation 2 into Equation 1.
Substituting Equation 2 into Equation 1:
400 = 2((w + 40) + w)
Simplifying:
400 = 2(2w + 40)
400 = 4w + 80
400 - 80 = 4w
320 = 4w
w = 320/4
w = 80
Now we have the value of 'w' (width) as 80 feet. We can substitute this value back into Equation 2 to find the length:
l = w + 40
l = 80 + 40
l = 120
Therefore, the width of the cattle enclosure is 80 feet, and the length is 120 feet.