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

[Q]: Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,6 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? 
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 5
[A]: d


[Q]: Problem: in right triangle abc , ac is the hypotenuse . if ac is 35 and ab + bc = 55 , what is the area of the triangle abc ? 
Options: a ) 225 , b ) 450 , c ) 25 √ 2 , d ) 200 , e ) 200 √ 2
[A]: b


[Q]: Problem: if the sides of a cube are in the ratio 5 : 3 . what is the ratio of their diagonals ? 
Options: ['a ) 5 : 9', 'b ) 9 : 3', 'c ) 5 : 4', 'd ) 3 : 5', 'e ) 5 : 3']
[A]:
e