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: what is the ratio between perimeters of two squares one having 2.5 times the diagonal then the other ? 
Options: a ) 4 : 5 , b ) 1 : 3 , c ) 2.5 : 1 , d ) 3.5 : 1 , e ) 3 : 2
Example Output: c

Example Input: Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ? 
Options: ['a ) 24', 'b ) 26', 'c ) 28', 'd ) 30', 'e ) 32']
Example Output: d

Example Input: Problem: if n is the smallest integer such that 864 times n is the square of an integer , what is the value of n ? 
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Example Output:
b