A farmer owns 1000 m of fence and wants to enclose the largest possible rectangular area. the region to be fenced has a straight canal on one side, and thus needs to be fenced on only three sides. what is the largest area she can enclose and what are its dimensions?

Question

Mathematics

Christian Rich

14 January, 21:21

A farmer owns 1000 m of fence and wants to enclose the largest possible rectangular area. the region to be fenced has a straight canal on one side, and thus needs to be fenced on only three sides. what is the largest area she can enclose and what are its dimensions?

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Answers (1)

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Kailee Hood · Answer 1

These questions are hard until you "translate" them into maths.

So this farmer wants to maximize the terratory enclosed by the fence.

The area of a rectangle is a*b where we know that a+2b=1000.

a+2b=1000

thus a=1000-2b

a*b = b * (1000-2b) and you need to find the maximum for this

=-b^2 + 1000b

Now you can do 2 things. Easy: use differentiation (if you know it)

Hard: Use the method of completing a square