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: in triangle pqr , the angle q = 90 degree , pq = 3 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 ) 3.6 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
b

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']
c

Problem: a crate measures 4 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ? 
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12

d