Archaeologists found part of the circular wall that surrounds an ancient
city. They measure the distances shown. The 272-m segment lies on a line
through the center of the circular wall. What was the diameter of the
circular wall?
310 m
805 m
272 m

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.