The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along it's two lengths and one-width is to be done at $50 per meter. If the total cost of fencing is $12000, what are the field's dimensions?
let the width be y m
and each of the lengths x m
so 2x + 2y = 300
x + y = 150
y = 150-x
cost = 50(2x+y+
= 50(2x + 150-x)
= 50x + 7500
then 50x + 7500 = 12000
50x = 4500
x = 90
y = 150-90 = 60
the field is 60 m by 90 m
Let's assume the length of the rectangular field is L and the width is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
In this case, the field is fenced along three sides only, which means only two lengths and one width will have fencing. So, the perimeter equation becomes: P = 2L + W.
Given that the perimeter is 300 meters, we can write the equation as: 300 = 2L + W. ---(Equation 1)
The cost of fencing is $50 per meter and the total cost is $12,000.
The cost of fencing the two lengths and one width can be calculated using the formula: Cost = (2L + W) * price per meter.
Substituting the given values, we have: 12000 = (2L + W) * 50.
Simplifying the equation, we get: 12000 = 100L + 50W. ---(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the dimensions of the field.
From Equation 1, we can isolate W and substitute it into Equation 2.
Rearranging Equation 1, we get: W = 300 - 2L.
Substituting this value of W into Equation 2, we get: 12000 = 100L + 50(300 - 2L).
Simplifying the equation, we get: 12000 = 100L + 15000 - 100L.
Combine like terms: 12000 = 15000.
This equation is not true, which means there is no solution to this problem.
Therefore, it seems there is an error in the given information, as the provided dimensions do not satisfy the given conditions and cost. Please double-check the information or provide additional details.
To find the dimensions of the rectangular field, we need to first set up equations based on the given information.
Let's assume the length of the rectangular field is L meters, and the width is W meters.
The perimeter of a rectangle is calculated by adding up all four sides. In this case, since the field is to be fenced along only three sides (two lengths and one width), the perimeter can be expressed as:
Perimeter = 2L + W
Given that the perimeter is 300 meters, we can write the equation as:
2L + W = 300 -- Equation (1)
Next, we need to calculate the cost of fencing the field. Since the cost of fencing is $50 per meter, we can express the total cost as:
Cost = (2L + W) * $50
Given that the total cost is $12000, we can write the equation as:
(2L + W) * $50 = $12000 -- Equation (2)
Now, we have a system of two equations (Equations 1 and 2) with two variables (L and W). We can solve this system of equations to find the dimensions of the rectangular field.
First, we rearrange Equation (1) to solve for W:
W = 300 - 2L
Then, substitute this value of W into Equation (2):
(2L + (300 - 2L)) * $50 = $12000
Simplifying:
(300 + 50L) * $50 = $12000
Dividing both sides by $50:
300 + 50L = $240
Subtracting 300 from both sides:
50L = $240 - $300
50L = -$60
Dividing both sides by 50:
L = -$60 / 50
L = -1.2
We obtain a negative value for L, which is not possible for the length of a rectangle. Hence, there seems to be an error in the given information. Please double-check the values provided for the perimeter, total cost, or cost per meter of fencing to resolve the inconsistency.