MathDB

The rectangular parallelepiped (box)

P

has some special properties. If one dimension of

P

were doubled and another dimension were halved, then the surface area of

P

would stay the same. If instead one dimension of

P

were tripled and another dimension were divided by

3

, then the surface area of

P

would still stay the same. If the middle (by length) dimension of

P

1

, compute the least possible volume of

P

12