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: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 3 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 9 : 10 , b ) 19 : 20 , c ) 29 : 30 , d ) 39 : 40 , e ) 49 : 50

SOLUTION: e

PROBLEM: Problem: rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ?
Options: ['a ) 13 1 / 2', 'b ) 20', 'c ) 18 3 / 4', 'd ) 21', 'e ) 24']

SOLUTION: b

PROBLEM: Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ' s area is 180 square feet and its length is 8 feet longer than its width . if the uniform width between the rug and room is 8 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: ['a ) 32', 'b ) 36', 'c ) 704', 'd ) 46', 'e ) 104']

SOLUTION:
c