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

[EX Q]: Problem: the sum of two numbers is 16 and the sum of their squares is 113 . find the numbers . 
Options: a ) 1 and 2 , b ) 4 and 5 , c ) 7 and 8 , d ) 2 and 3 , e ) 6 and 7
[EX A]: c

[EX Q]: 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
[EX A]: e

[EX Q]: Problem: 108 . triangle a ’ s base is 12 % greater than the base of triangle b , and a ’ s height is 12 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ? 
Options: a ) 9 % less , b ) 0.7 % less , c ) equal to each other , d ) 1 % more , e ) 9 % more
[EX A]:
b