Guard Dogs

1
Guard Dogs

• An Investigation

2

• Guard Dogs
• A security firm uses a
• guard dog to look after a compound.
• The compound is a rectangular
• area measuring 90m by 40m
• as shown in the diagram.
• 
  
• On the first night, the
• 
  dog is attached to a 40m chain
  which
• 
  is tethered to the wall at point A.
• 
  Draw a diagram showing the
  area which
• 
  the dog can patrol and
  calculate this area.

3

• On the second night the dog is
• tethered at point B halfway
• down one wall.
• Show and calculate the new
• area which the dog can patrol.
• 
  After a breakout from the compound, it is
• 
  decided to introduce a second dog.
• 
  This dog is also on a 40m chain.
• 
  The dogs are tethered to the walls as
• 
  shown.
• Calculate the area now patrolled by the dogs.
• Are these the most effective positions to put the
  dogs in or can you think of a better arrangement
  which would allow the dogs to patrol a greater
  area of the compound?

4

• Solution
• First area 1256 sq.metres
• Second area 1400.7 sq.metres
• Two dogs 2656.7