Science & Mathematics - 14 December 2006

A farmer wishes to build a rectangular sheep pen with a 160m fence,using one side of an existing shedas the side.The side is also rectangular of measurement 20 m x 20 m.

a)Find the measurement and the area of the sheep pen if one sideof 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 shed as part of thewidth of the sheep pen,find the length and width of the sheep pen with maximum area.

c)If two sheep pen of the same size are built adjusted to each other,find
1)the length of the new sheep pen if one side of the shed is used as the width of the sheep pen.
(2)the length and width of the sheep pen,which is adjusted so that enclosed area are maximum.

d)Find the maximum enclosed area if the same fence is used to construct three rectangular sheep pens.

Further Ivestigation

If n rectangular sheep pens of width 20 m are constructed(one side of the existing shed is used as part of the pen)from a fence of length x m,find in term of x and n :

(1)the length of the sheep pen,
(2)total area of the sheep pens.

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