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A farmer needs to enclose three sides of a garden with a fence (the fourth side is a cliff wall). The farmer has 43 feet of fence and wants the garden to have an area of 228 sq-feet. What should the dimensions of the garden be? (For the purpose of this problem, the width will be the smaller dimension(needing two sides); the length will be the longer dimension (needing one side). Additionally? The length should be as long as possible.)

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sqdancefan

Answer:

  9.5 ft wide by 24 ft long

Step-by-step explanation:

A graphing calculator shows there are two solutions to the system of equations ...

  2x + y = 43 . . . . . . fence length when x= width

  xy = 228 . . . . . . .  area

The solutions are ...

  (width, length) = (9.5, 24)   or   (12, 19)

Since we want the length as long as possible, the choice of dimensions is ...

  length = 24 feet; width = 9.5 feet.

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