I find the following problem very hard!

A rectangular box has 3 faces in the planes given by , and . The vertex that is not in the latter planes is in the plane . Determine the dimensions that maximizes the volume of the box.

I tried to visualize the box by drawing a sketch and I think I couldn't. So I'm stuck on giving an expression of the volume of the box. I'd like some help for this task.

Precisely I've drew a rectangular parallelepiped in the xyz plane but I don't see how it could have a maximum volume so I think I drew it wrongly.