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: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 54 square centimeters , what is the length of the rectangle in centimeters ? 
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
d

Problem: if the height of a cone is increased by 160 % then its volume is increased by ? 
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 160
e

Problem: what is the smallest positive perfect square that is divisible by 12 , 14 , and 42 ? 
Options: a ) 900 , b ) 1089 , c ) 1600 , d ) 1764 , e ) 2025

d