Estimate the length, width, and height of a bedroom. If bedroom is empty, the volume is 864 cubic meters. The room's L=W. The height is 1/2 the length and width.

Let the length be x

It is given that length = width

So, width = x

Also given that height is half of length.

So height = x/2

The bedroom has shape of cuboid.

So, volume = length * width * height = x*x*(x/2) = (x^3)/2

Given volume = 864 m^3

So,

(x^3)/2 = 864

x^3 = 864*2

x^3 = 1728

x = (1728)^{1/3}

x = 12

Hence,

Length = x = 12 m

Width = x = 12 m

Heght = x/2 = 12/2 = 6m

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