Final answer:
To find the dimensions of the rectangle that maximize the enclosed area, we need to use the given information about the amount of fencing available, and apply optimization techniques.
Step-by-step explanation:
To find the dimensions of the rectangle that maximize the enclosed area, we need to use the given information about the amount of fencing available. Let's assume the length of the rectangle is x yards. In this case, the width will be (2000 - 2x) yards (since the total fencing length is 2000 yards and two lengths of the rectangle are used). The area of the rectangle is given by the equation:
A = x(2000 - 2x)
By expanding and simplifying the equation, we get:
A = 2000x - 2x^2
To find the dimensions that maximize the area, we take the derivative of the area equation with respect to x and set it equal to 0, then solve for x. Once we find the value of x, we can calculate the corresponding width and area of the rectangle.