## Solving Pallet Equations

A recent delivery came with an unexpected bonus.

A diagram illustrating the geometric relationship between the length and the width of the box!

Of course, the equation $3w = 2l$ immediately came to mind.  I also noticed that the pallet could not be a square:  if $3w = l + 2w$, then $w = l$, which would make the box itself a square-based box, which it clearly is not.

I did a quick search and found the standard pallet size to be 48 inches by 40 inches.  So my best guess is that $w = 12$ and $l = 18$.  This box has already been discarded, so I guess I’ll have to order another box to find out!