In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Example Input: Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x and y coordinates of p , q and r are to be integers that satisfy the inequalitites - 4 ≤ x ≤ 5 and 6 ≤ y ≤ 16 . how many different triangles with these properties could be constructed ? 
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Example Output: c

Example Input: Problem: a rectangular garden is to be twice as long as it is wide . if 900 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ? 
Options: a ) 40 , b ) 50 , c ) 60 , d ) 200 , e ) 300
Example Output: e

Example Input: Problem: the number 150 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? 
Options: a ) 17 , b ) 18 , c ) 15 , d ) 14 , e ) 13
Example Output:
b