In the figure above,
The areas of the three sides are given by \(HW, HL,\) and \(LW\).
Assuming \(HW=12 = (3)(4), HL = 15 = (3)(5),\) and
\(LW= 20 = (5)(4),\)
it is clear that possible choices for the edge lengths are
\(H= 3, W=4, \)and \(L =5\)
Therefore, the volume of the rectangular solid is
Edit: For an alternative method (and a good one), kindly check KARTIK's comment.