Answer:
112 in³
Step-by-step explanation:
We assume the side areas are of just one of the two sides with equal area.
Consider the areas to be a, b, c in terms of box dimensions x, y, z:
a = xy; b = yz; c = xz
Then the product of the areas is ...
abc = (xy)(yz)(xz) = x²y²z²
and the volume of the box is ...
V = xyz = √(x²y²z²) = √(abc)
V = √((14 in²)(16 in²)(56 in²)) = √(12544 in⁶)
V = 112 in³
The volume of the box is 112 cubic inches.
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The dimensions of the box could be 2 in by 7 in by 8 in.
