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^{2} x B^{2} 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. QED.