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The fence will go a distance x perpendicularly away from the banks of the river at two places, with a stretch of fence in between, parallel to the river, and measuring 1000-2x meters.
The area fenced in is
The quadratic function
, like all quadratic functions
, has a maximum (and line of symmetry) at
In this case, the maximum and line of symmetry are at
So, 250 meters will be the width of the rectangular plot.
The length of the rectangular plot (along the river) will be (in meters)
and the area (in square meters) will be