Margaret has some left over carpet after she finished remodeling her house. She would like to make an elliptical rug with the leftover carpet. She sketches two foci inches from the center of the ellipse on a piece of paper. In order to determine the shape of the ellipse, she loops a pencil through a string that is inches long and fixes the ends of the string at two foci. Determine the longest and shortest lengths of the elliptical rug.