# math

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a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rect angular piece of ground that is as large as possible. the land is bordered by water on two sides.

There are three options for the farmer
Option 1) have two sides bordered by the water and two sides by the fence
Option 2) have one side bordered by water and three sides by the fence
Option 3) use fence for all four sides

Construct formula for the area in each of the three options( hint: name one side x)

• math -

(1)
The sides are x and y, so y = 400-x
The area is thus a = xy = x(400-x)

(2)
If the side x is parallel to the water,
x+2y = 400, so y = (400-x)/2 and the area is
a = xy = x*(400-x)/2

(3)
x+y=200, so the area is
a = xy = x(200-x)

If you need to find the maximum area, just remember that the graph of a is a parabola, with max area at the vertex. So, find the vertex of each parabola.

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