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Is there a way to reconstruct a rectangular prism with this information?

Asked by PhiNotPi (12677points) October 23rd, 2011

Is there a way to reconstruct a rectangular prism if you know its volume, surface area, and total combined edge length? It does not matter if the dimensions are swapped (a 1×2x3 rectangle is the same as a 3×1x2).

v = abc
s = 2ab + 2ac + 2bc
e = 4a + 4b + 4c
(v,s,e are known. a,b,c are not.)

This is NOT homework.

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