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Exercise 50
1A farmer wishes to enclose a rectangular
field of area 100 m². The farmer must buy
fencing material for three of the sides, but
the fourth side (one of the longer sides) will
be an existing fence.
The shorter sides of the rectangular
enclosure are to have length x m.
Write down the length of the longer
sides of the enclosure, in terms of x.
b) Find an expression, in terms of x, for the
total length of new fencing the farmer
must buy to enclose the rectangular field.
Find the minimum length of fencing
required, and the value of x for which
this minimum occurs.
Sketch a graph of fencing length against
x to confirm your answer.
​

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