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: 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

SOLUTION: a

PROBLEM: Problem: if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is : 
Options: ['a ) 15 : 12', 'b ) 15 : 14', 'c ) 15 : 16', 'd ) 15 : 22', 'e ) none of these']

SOLUTION: c

PROBLEM: Problem: what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ? 
Options: ['a ) 36', 'b ) 14', 'c ) 12', 'd ) 15', 'e ) 11']

SOLUTION:
a