Question 12
A fenced, rectangular field measures $24$ meters by $52$ meters. An agricultural researcher has $1994$ meters of fence that can be used for internal fencing to partition the field into congruent, square test plots. The entire field must be partitioned, and the sides of the squares must be parallel to the edges of the field. What is the largest number of square test plots into which the field can be partitioned using all or some of the $1994$ meters of fence?