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

[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
[A]: c


[Q]: Problem: the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ? 
Options: ['a ) 3 x', 'b ) 4 x', 'c ) 9 x', 'd ) 12 x', 'e ) 27 x']
[A]: b


[Q]: Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 64 , what is the measure of side xy ? 
Options: a ) 4 , b ) 16 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
[A]:
b