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

Example Input: Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 49 . find the ratio of their corresponding heights . 
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 4 / 7 , e ) 2 / 3
Example Output: d

Example Input: Problem: in triangle pqr , the angle q = 90 degree , pq = 2 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz 
Options: a ) 1.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Example Output: a

Example Input: Problem: if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ? 
Options: a ) 4 , b ) 8 , c ) 12 , d ) 3 , e ) 18
Example Output:
d