A box contains 12 1/2 square feet of tiles and cost $40.21. What is the approximate price per square foot?

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 15.

The measures of the legs of a right triangle are 15m and 20m . what is the length of the hypotenuse

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.