The Field

1
The Field

• An Investigation

2

• The Field
• The drawing (which is NOT drawn to scale) shows a
  field.
• The area of the field is 8000 square metres.
• The field is in the shape of a trapezium.
• The wider end is 82 metres
• long, and the narrower
• end is 54 metres long.
• The dotted line is a fence which divides the
  field into two parts which are equal in area.
• How far is the fence from the wide end? Give
  your answer to the nearest metre.

3
Exercise

• If the field was to be divided into three equal
  parts using two parallel fences, where would
  these fences need to be placed in the field?

4
Solution

• Length of baseline 117.65m
• Let x be length from 82m side to fence and h the
  length of the fence.
• Obtain from the left part
  and
• from the other part. Putting these equal leads to
  the quadratic equation
• 28x2 19294.2x 941200 0 , which solves to
  give
• x 52.83 This gives h 69.43