Let's call the width of the plot x feet.
Since the side along the river does not need to be fenced, this means that we only need to consider three sides of the plot - the two ends and the back. Therefore, the length of the plot will be 800 - 2x feet.
To find the area of the plot, we multiply the length by the width:
Area = (800 - 2x) * x
To maximize the area, we can take the derivative of the area function with respect to x and set it equal to zero:
d/dx [(800 - 2x) * x] = 800 - 4x = 0
Solving for x:
4x = 800
x = 200
So, the width of the plot is 200 feet.
The length of the plot is 800 - 2(200) = 400 feet.
The largest area that can be enclosed is 200 * 400 = 80,000 square feet.
You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? River X 800 - 2x The width, labeled x in the figure, is (Type an integer or decimal.) feet The length, labeled 800 - 2x in the figure, is feet. (Type an integer or decimal.) The largest area that can be enclosed is (Type an integer or decimal.) square
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