Science & Mathematics - 27 October 2006

A farmer wishes to build a rectangular sheep pen with a 160m fence, using one side of an existing shed as the side. The shed is also rectangular of measurement 20m x 20m.
a.)Find the measurement and the area of the sheep pen if one side of the existing shed is used as the width of the sheep pen.
b.) By using the fence of the same length and using the width of the sheep pen with maximum area.
c.)If two sheep pens of the same size are built adjacent to each other, find
i.)the length of the new sheep pen if one side of the shed is used as the width of the sheep pen.
ii.) the length and width of the sheep pen, which is adjusted so that the enclosed area is maximum.
d.)Find the maximum enclosed area if the same fence is used to construct three rectangular sheep pens..
e.)If n rectangular sheep pen of width 20m are constrcuted(1 side of the existing shed is used as part of the pen) from a fence of length x m, find in terms of x and n:
i.)the length & total area of the sheep pen

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