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

Input: Consider Input: 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 100,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7

Output: d

Input: Consider Input: Problem: if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26

Output: c

Input: Consider Input: Problem: if the sides of a cube are in the ratio 9 : 5 . what is the ratio of their diagonals ?
Options: a ) 9 : 5 , b ) 16 : 9 , c ) 4 : , d ) 3 : 4 , e ) 3 : 8
Output: a