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A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?

Does that mean I have to consider it a triangle?

  • Math -

    No, make the river one of the side, fence the other three sides.

    Area= LW
    or L=8000-2W
    Area= W(8000-2W)= 8000w-2W^2

    You can find the max several ways, graphing is simple. IF you get stuck, repost.

  • Math -

    Thanks. I'm still confused though. I'm not sure how you got
    Area= W(8000-2W)= 8000w-2W^2

    What happened to the L

    Do I need a system of equations?

    Sorry, this has got me stumped.

  • Math -

    It is a quadratic.
    Let y= 8000x-2x^2

    graph y vs X on your graphing calc, notice where the max is on x

    Second method. The parabola goes up to a max then down. Find the intercepts for y=0, those will be symettrical to the parabolic axis, so look for where the midpoint of the intercepts are.
    intercepts x=0 , x=4000, so the max will be at x (or width 2000).
    then solve for L (8000-2W).
    Third method:
    Calculus (in a few years you will master this, just watch now)
    Area= 8000x-2x^2
    d Area/dx=0= 8000-4x
    solve for x, x=2000 at max.

  • Math -

    Ok, thanks so much for your explanations.

    So, is the max area 8,000,000?

  • Math -

    can you help me with this homework please

  • Math -

    What don't you understand?

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