**Answer:**
Width=40, height=20, depth=18.

If we call the height H, the width W and the depth D we have:

H x W = 800 (so H = 800 ÷ W) (1)

W x D = 720 (so W = 720 ÷ D) (2)

H x D = 360 (so H = 360 ÷ D) (3)

Using (1) and (3) we have:

800 360

--- = ---

W D

800 x D = 360 x W

Using (2):

800 x D = 360 x 720

---

D

800 x D^{2} = 259,200

D^{2} = 324

D = 18

Using (2), W = 40.

Using (1), H = 20. QED.