Guard Dogs An Investigation

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. Compound 40m 90m 40m 90m A

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? 40m 90m B

Solution First area = 1256 sq.metres Second area = sq.metres Two dogs =