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

Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 16 cm 2 . find the lengths of all sides . 
Options: a ) 10 and 3 , b ) 9 and 6 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
b

Problem: what is the smallest positive integer x , such that 7000 x is a perfect cube ? 
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
d

Problem: if the sides of a cube are in the ratio 5 : 4 . what is the ratio of their diagonals ? 
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 4 : 7 , d ) 3 : 4 , e ) 4 : 5

b