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

Input: Consider Input: Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ? 
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824

Output: b


Input: Consider Input: Problem: one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square 
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140

Output: c


Input: Consider Input: Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ? 
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29


Output: a