Given that the relationship between the length and width of the rectangular field is 3 to 2, and that said field is 150 yards long, the following calculation must be performed to determine its width:
((150/3) x 2) = X
50 x 2 = X
100 = X
Thus, the common largest divisor between both numbers is obtained, and the relationship from 3 to 2 is established based on said number. Therefore, the rectangular field is 100 yards wide by 150 yards long.