The length and width that will maximize the area are 175 ft and 87.5 ft respectively
The largest area that can be enclosed is 15312.5 ft²
where
l = length
w = width
The fencing is 350 ft it is use to enclose a rectangular plot with a river occupying one part.
Therefore,
perimeter = l + 2w
350 = l + 2w
l = 350 - 2w
area = (350 - 2w)w
(350 - 2w)w = 0
where
w = 0 or 175
average = 175/2 = 87.5
Hence, the max area is at w = 87.5 ft
Therefore,
l = 350 - 2(87.5) = 175 ft
length = 175 ft
width = 87.5 ft
Therefore,
area = 175 × 87.5 = 15312.5 ft²
Therefore, the largest area that can be enclosed is 15312.5 ft²
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