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Nabu's Knee-knocker SignSolution


  1. TWO PENS

    The largest possible total area is 600 m2.

    Each pen is 20 m by 15 m. (See the table of other possibilities in the hint.)


  2. THREE PENS

     
    The largest possible total area is 450 m2.

    Each pen is 15 m by 10 m.

    Here is a table showing other possible dimensions and the resulting total areas.




    FOUR PENS

    The largest possible total area is 360 m2.

    Each pen is 12 m by 7.5 m.

    Here is a table showing other possible dimensions and the resulting total areas.




  3. To build several rectangular pens with 120 meters of fencing and with as large a total area as possible:

    • use half of the fencing for the common sides and corresponding ends (blue segments in picture). There is one more such side than the number of pens, so divide 60 by (n+1)-n being the number of pens.

    • use half of the fencing for the non-common sides (red segments in picture). So, the total length of the pens will always by 30 meters.


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