What is the length of the longest stick that can be placed in a rectangular box with dimensions 6 cm, 8 cm and 24 cm?

The longest stick that could be placed in the rectangular box of
dimension 6cm , 8cm and 24cm is the diagonal of the box.

To find the
diagonal of the box, first we find the bottom surface  diagonal:

We
imagine that the box has the bottom surface with length 8cm and  width
6cm.

Therefore the diagonal d of the bottom surface is given
by:

d^2 = 6^2+8^2 = 100.

The height h
of the box : h  = 24.

Therefore the diagonal D of the box is the
line from one corner  of the bottom surface to to the opposite corner on the top
surface.

The diagonal D of the the box is got
by:

D^2 = d^2+h^2,  where h = heght of the bos which is
24.

Therefore D^2 = d^2+h^2 = 100 +24^2 = 100 + 576 =
676.

Therefore D = sqrt(676) = 26.

So
the longest stick that could be placed in the box = 26cm.