What is the longest stick that can be placed in a box 15 cm long, 20 cm wide, and 60 cm high?

Make right triangles

find the length of the diagonal on the ground then find the length of the diagonal from corner to corner (see diagram

actually, I found a neat thing

see diagram

remember the pythagorean theorem
so, if the legs of a right triangle=a and b and the hyptonuse is c then
a²+b²=c²

alright, so we look at the diagram now
a²+b²=k²
and
c²+k²=d²

but, k²=a²+b²
so
a²+b²+c²=d²
a=15
b=20
c=60

15²+20²+60²=d²
225+400+3600=d²
4225=d²
65=d

the longest stick is 65cm assuming it has no width