The hypotenuse of a right triangle measures 19 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

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.