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

[EX Q]: Problem: what is the smallest positive integer x such that 864 x is the cube of a positive integer 
Options: a ) 6 , b ) 12 , c ) 9 , d ) 5 , e ) 2
[EX A]: e

[EX Q]: Problem: the ratio of the areas of two squares , one having double its diagonal then the other is : 
Options: ['a ) 2 : 1', 'b ) 1 : 2', 'c ) 2 : 3', 'd ) 1 : 4', 'e ) 4 : 1']
[EX A]: e

[EX Q]: Problem: the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square ? 
Options: a ) 5 : 24 , b ) 5 : 19 , c ) 5 : 13 , d ) 5 : 22 , e ) 5 : 18
[EX A]:
a