Daryll is given $30 and spends $1.25 per day on basketball cards. On the same day, Larry is given $2 and saves $1.25 per day. The graph shows the amount of money each boy has compared to the number of days that have passed.

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.