The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at $50 per meter. If the total cost of fencing is $12,000, what are the field’s dimensions?
2w+2l=300
(w+2l)*50 = 12000
width=60
length=90
To solve this problem, we need to understand the relationship between the perimeter of a rectangular field, the cost of fencing, and the dimensions of the field.
Let's start by defining the variables:
- Let L be the length of the rectangular field.
- Let W be the width of the rectangular field.
The perimeter of a rectangle can be calculated using the formula:
Perimeter = 2 * (Length + Width)
In this case, the perimeter of the field is given as 300 meters. So we can write the equation as:
300 = 2 * (L + W)
Now let's consider the cost of fencing. The cost is given as $12,000 and the fencing is done at $50 per meter. Since we are fencing along three sides only (two lengths and one width), the total cost can be calculated as:
Total Cost = Cost per meter * (2 * Length + Width)
In this case, the total cost is given as $12,000 and the cost per meter is $50. So we can write the equation as:
12000 = 50 * (2L + W)
Now we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of L and W.
First, let's simplify the equations:
Equation 1: 300 = 2L + 2W
Equation 2: 12000 = 100L + 50W
Next, we can rewrite Equation 1 in terms of L:
Equation 1: 150 = L + W
Now we can substitute Equation 1 into Equation 2:
12000 = 100(L + W) + 50W
12000 = 100L + 100W + 50W
12000 = 100L + 150W
From Equation 1, we can substitute the value of L into the above equation:
12000 = 100(150 - W) + 150W
12000 = 15000 - 100W + 150W
12000 = 15000 + 50W
12000 - 15000 = 50W
-3000 = 50W
W = -3000/50 = -60
The width of the field cannot be negative, so there seems to be an error in the calculations. Please check the given information to ensure its accuracy.