There are 30 people at a meeting, They each shake hands with everyone. How many handshakes were there? Hint: Think "The number of combinations of 30 people at a
meeting giving handshakes to each other 2 at a time."

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.