You are given a string of fixed length l with one end fastened at the origin, and you are to place the string in the xy plane with its other end on

You are given a string of fixed length l with one end fastened at the origin, and you are to place the string in the xy plane with its other end on the x axis in such away as to enclose the maximum area between the string and the x axis. Show that the required shape is a semi-circle