by Ian Kay
My square garden has sides that are whole numbers of metres and is surrounded by a fence with posts at its four corners and at one metre intervals along its sides. I have chosen a post on each of the sides and stretched a string around these to form four triangular beds surrounding a lawn with four sides of different lengths. I can do this in a number of ways but it turns out that the string needed to do this has only two possible lengths.
What is the area of my lawn If I choose the arrangement with the smaller length string?