Canada Post accepts international parcels whose (Length+Girth) is less than or equal to 2 meters, and Length is less than or equal to 1 meter. Girth is defined as the perimeter of the cross section. We wish to ship a parcel of the shape of a triangular prism of length l meters. The cross section is a right triangle with catheti of lengths a and b meters. Assume the package walls are thin. What is the maximal volume of a parcel?

I provided a drawing via paint for you to envision my take on the problem

Hence,

Boundaries:

The critical points of the gradient of the volume equation comes up with (0, 0, 0), hence it is of no use. Okay, I have not had much experience with Lagrange multipliers, but here is my attempt.

Hence, let

The critical points of L are determined via

At this point the system of equations look quite nasty, and moreoever I have been told that there is an easier route to solving this problem. Can someone suggest something?