TASK DEFINITION: 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: Problem: a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6

SOLUTION: b

PROBLEM: Problem: if the length of the side of a square is doubled , what is the ratio of the areas of the original square to the area of the new square ? 
Options: ['a ) 1 : 4', 'b ) 2 : 4', 'c ) 3 : 4', 'd ) 4 : 4', 'e ) 5 : 4']

SOLUTION: a

PROBLEM: Problem: a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle e in terms of h ? 
Options: ['a ) h / √ 2', 'b ) h / 2', 'c ) h / 4', 'd ) ( h ) ^ 2', 'e ) ( h ) ^ 2 / 4']

SOLUTION:
e