Richard is building a rectangular backyard from 360 feet of fencing. the fencing must cover three sides of the backyard (the fourth side is bordered by richard's house). what is the maximum area of this backyard?

  16200 ft²

Step-by-step explanation:

The maximum area is obtained when half the fence is parallel to the house, and the other half is used for the ends of the rectangle. The resulting area will be 180 ft long by 90 ft wide, or ...

  (180 ft)(90 ft) = 16200 ft²

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Let x represent the length of the fence parallel to the house. Then the ends of the rectangular backyard will have length (360-x)/2, and the total area will be ...

  A = x(360 -x)/2

This describes a parabola opening downward with zeros at x=0 and x=360. The vertex is halfway between the zeros, at x = 180. This is the value of x that gives the maximum area.