Suppose you want to fence in some land along the edge of a straight river. the fenced area will be in the shape of a rectangle, and the side along the river will not be fenced. you have 950 meters of fencing to use. what will be the dimensions of the fenced-in region that has the largest area?

For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.

The dimensions are 475 m by 237.5 m.

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Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.