The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu.

Consider l, b and h are the length, breadth and height of the room.

So, b = 2h and b = (1/2)l

⇒ l/2 = 2h

⇒ l = 4h

⇒ l = 4h, b = 2h

Now, Volume $=512 \mathrm{dm}^{3}$

⇒ 4h ∗ 2h ∗ h = 512

$\Rightarrow h^{3}=64$

⇒ h = 4

So, Length of the room (l) = 4h = 4 * 4 = 16 dm

Breadth of the room (b) = 2h = 2 * 4 = 8 dm

And Height of the room (h) = 4 dm.