When a triangle is inscribed in a semicircle where a diameter of the circle is a side of the​ triangle, the triangle formed is always a right triangle. If an isosceles triangle​ (two equal​ sides) is inscribed in a semicircle with a radius of 9 ​inches, find the length of the two legs of the triangle.

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.