a rectangular lot whose perimeter is 1600 feet is fenced on three sides. An expensive fencing along the lot's length cost $20 per foot, and an inexpensive fencing along the two side widths costs $5 per foot. The total cost of fencing along the three sides comes to $13000. What are the lot's dimensions?
s = side length
x = long length
2 s + x = 1600 so x = (1600-2s)
2 s (5) + x (20) = 13,000
10 s + 20 (1600-2s) = 13,000
S= 1900/3
X= 1600-(1900/3)
Let's assume that the length of the lot is L feet and the width is W feet.
Given that the perimeter of the lot is 1600 feet, we can form the equation:
2L + W = 1600 ----(1) (since there are three sides, two lengths and one width)
The cost of fencing along the lot's length is $20 per foot and the cost of fencing along the two side widths is $5 per foot.
The total cost of fencing the three sides is $13000. We can form the equation:
20L + 5W + 5W = 13000 ----(2)
Simplifying equation (2), we get:
20L + 10W = 13000
Dividing both sides by 10, we get:
2L + W = 1300 ----(3)
Now, we can solve equations (1) and (3) simultaneously to find the values of L and W.
Subtracting equation (1) from equation (3), we get:
2L + W - (2L + W) = 1300 - 1600
Simplifying, we get:
0 = -300
This indicates that the equations are inconsistent, and there is no real solution.
Therefore, there is no rectangular lot that satisfies the given conditions.
To solve this problem, we need to set up and solve a system of equations based on the given information.
Let's assume that the length of the rectangle is 'L' feet, and the width of the rectangle is 'W' feet.
Given that the perimeter of the rectangle is 1600 feet, we can write the equation:
2L + W = 1600 (Equation 1)
Now, let's calculate the cost of the fencing along the three sides.
The expensive fencing along the length of the rectangle costs $20 per foot, so the cost of this fencing would be 20 * L.
The inexpensive fencing along the two side widths costs $5 per foot, so the cost of this fencing would be 5 * 2 * W.
Given that the total cost of fencing is $13000, we can write the equation:
20L + 5 * 2W = 13000 (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of L and W.
Let's solve this system of equations:
2L + W = 1600 (Equation 1)
20L + 5 * 2W = 13000 (Equation 2)
We can solve Equation 1 for W:
W = 1600 - 2L
Substitute this value of W into Equation 2:
20L + 5 * 2(1600 - 2L) = 13000
20L + 5 * (3200 - 4L) = 13000
20L + 16000 - 20L = 13000
16000 = 13000
This equation is not valid, and it means there is no solution to this system of equations. Therefore, there is no valid length and width that satisfies all the given conditions.
Hence, there are no dimensions for the rectangular lot that satisfy the given conditions.