a fence has 200m of fencing to enclose two adjacent rectangular fences .find the dimensions such that the area enclosed will be 1400 square metre
2x+3y=200
2xy=1400
2x+3(700/x) = 200
x=88.08 or 11.92
So, the area is
23.84 x 58.72
or
176.16 x 7.94
To find the dimensions of the adjacent rectangular fences that will enclose an area of 1400 square meters, we need to set up and solve an equation based on the given information.
Let's assume that the length of one rectangle is x meters. Since two rectangles are adjacent, the other rectangle will also have a length of x meters.
The total perimeter of the two rectangles is equal to the amount of fencing available, which is 200 meters. The formula for the perimeter of a rectangle is:
Perimeter = 2*(length + width)
For the first rectangle:
Perimeter = 2*(x + width)
For the second rectangle:
Perimeter = 2*(x + width)
Since the two rectangles are adjacent, the combined total perimeter is equal to 200 meters:
2*(x + width) + 2*(x + width) = 200
Simplifying the equation:
4*(x + width) = 200
x + width = 50
Now, we need to find the dimensions that will enclose an area of 1400 square meters. The formula for the area of a rectangle is:
Area = length * width
Since both rectangles have the same width, let's assume the width is y meters.
For the first rectangle:
Area = x * y
For the second rectangle:
Area = x * y
Since both rectangles are adjacent, the combined total area is equal to 1400 square meters:
(x * y) + (x * y) = 1400
Simplifying the equation:
2xy = 1400
xy = 700
Now, we have two equations:
x + width = 50
xy = 700
Using substitution, we can express width in terms of x:
width = 50 - x
Substituting this into the second equation:
x(50 - x) = 700
Expanding and rearranging the equation:
50x - x^2 = 700
x^2 - 50x + 700 = 0
Now, we can factor or use the quadratic formula to solve for x.
Since this equation does not factor easily, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -50, and c = 700. Plugging in these values:
x = (-(-50) ± √((-50)^2 - 4(1)(700))) / (2(1))
x = (50 ± √(2500 - 2800)) / 2
x = (50 ± √(-300)) / 2
Since we can't take the square root of a negative number in this context, it means that there are no real solutions for x.
Therefore, it is not possible to enclose an area of 1400 square meters with 200 meters of fencing in the given scenario.
To find the dimensions of the rectangular fence, we need to use the given information that the fence has a total length of 200 meters and the area enclosed should be 1400 square meters.
Let's assume that the length of one rectangular fence is 'x' meters. Since the two rectangular fences are adjacent, the length of the other rectangular fence will also be 'x' meters.
Now, let's consider the width of each rectangular fence. To find the width, we can subtract twice the length ('x') from the total length of the fence (200 meters). This is because each rectangular fence will share one length with the other fence, so we subtract 'x' twice.
Width = (Total Length - 2 * Length)
Width = 200 - 2x
The area of a rectangle can be found by multiplying its length and width. So, the area of one rectangular fence will be:
Area = Length * Width
Area = x * (200 - 2x)
Given that the area should be 1400 square meters:
x * (200 - 2x) = 1400
Now, let's solve this equation to find the value of 'x':
200x - 2x^2 = 1400
Rearranging the equation:
2x^2 - 200x + 1400 = 0
Now, we can solve this quadratic equation in order to find the value(s) of 'x'. We can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
By substituting the values of 'a', 'b', and 'c' into the formula, we can calculate the value(s) of 'x'.
Once we have the value(s) of 'x', we can substitute it back into the equation for the width to find the corresponding width value(s). And finally, we have the dimensions of the rectangular fence.