The dimensions of the box are:-Length=20, depth=12, height=15.

This is easily solved with a little simple algebra. If we call the three sides A, B, and C we have:

A x B = 240
A x C = 300
B x C = 180

Multiplying these together we get:

   (A x B) x (A x C) x (B x C) = 240 x 300 x 180

   A2 x B2 x C2 = 12,960,000

   (A x B x C)2 = 12,960,000

Which means that:

   A x B x C = 3600

Substituting A x B = 240 back in gives C = 15 and the rest follow.