instruction:
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
question:
Problem: the value of " a " varies in inverse proportion as the square of " b " . if the value of " a " is equal to 40 when " b " is equal to 12 . what would be the value of " a " when " b " is equal to 24 ?
Options: ['a ) 10', 'b ) 88', 'c ) 26', 'd ) 27', 'e ) 28']
answer:
a

question:
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
answer:
b

question:
Problem: the area of a parallelogram is 243 sq m and its altitude is three times the corresponding base . what is the length of the base ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 4 , e ) 12
answer:
b