a rectangular lot whose perimeter is 440 feet is fenced along three sides. an expensive fencing along the lot's length cost $16 per foot, and an inexpensive fencing along the two side widths costs only $11 per foot. The total cost of the fencing along the three sides comes to $4060. What are the lot's dimensions?
if width=x and length=y,
2x+2y = 440
2*11x + 16y = 4060
22x + 16(220-x) = 4060
6x = 540
x = 90
y = 130
To solve this problem, we need to set up equations based on the given information and then solve them to find the dimensions of the lot.
Let's assume that the length of the lot is L feet and the width is W feet.
We know that the perimeter of a rectangle is calculated by adding all four sides, so we can set up the equation:
2L + W = 440 (Equation 1)
We also know that the total cost of the fencing along the three sides is $4060. The cost of the expensive fence along the length is $16 per foot, so the cost of the length fence is 16L. The cost of the inexpensive fence along the two widths is $11 per foot, so the cost of the width fences is 2W. We can set up the second equation:
16L + 11(2W) = 4060
16L + 22W = 4060 (Equation 2)
We now have two equations with two variables (L and W). We can solve this system of equations using substitution or elimination. Let's use the substitution method:
From Equation 1, we can simplify it to express W in terms of L:
W = 440 - 2L
Substitute this value of W into Equation 2:
16L + 22(440 - 2L) = 4060
16L + 9680 - 44L = 4060
-28L + 9680 = 4060
-28L = -5620
L = (-5620)/(-28)
L = 200
Now substitute the value of L back into Equation 1 to solve for W:
2(200) + W = 440
400 + W = 440
W = 440 - 400
W = 40
Therefore, the dimensions of the lot are 200 feet by 40 feet.
Let's assume the length of the rectangular lot is L feet and the width is W feet.
Given that the perimeter of the lot is 440 feet, we can express this as:
2L + W = 440 (Equation 1)
We are also given that the total cost of the fencing along the three sides is $4060.
The cost of the expensive fencing along the length is $16 per foot. So, the cost of fencing along the length would be 16L.
The cost of the inexpensive fencing along the widths is $11 per foot, and since there are two side widths, the cost along the widths would be 2 * 11W = 22W.
Therefore, the total cost of the fencing is: 16L + 22W = 4060 (Equation 2)
We have two equations with two variables. Let's solve this system of equations to find the dimensions of the lot.
First, let's solve Equation 1 for W:
W = 440 - 2L
Now, substitute this value of W into Equation 2:
16L + 22(440 - 2L) = 4060
16L + 9680 - 44L = 4060
-28L = -5620
L = 200
Substitute this value of L back into Equation 1 to find W:
2(200) + W = 440
400 + W = 440
W = 40
Therefore, the dimensions of the lot are:
Length = 200 feet
Width = 40 feet