Answer:
[tex]20\sqrt5[/tex]
Explanation:
According to the question
[tex]2lb+2bh+2hl=94[/tex]
[tex]4l+4b+4h=48\\\Rightarrow 4(l+b+h)=48\\\Rightarrow l+b+h=12[/tex]
Length of the diagonal is given by
[tex]d=\sqrt{l^2+b^2+h^2}[/tex]
This can be also written as
[tex]d=\sqrt{(l+b+h)^2-(2lb+2bh+2hl)}\\\Rightarrow d=\sqrt{12^2-(94)}\\\Rightarrow d=\sqrt{144-94}\\\Rightarrow d=\sqrt{50}=5\sqrt2\ in[/tex]
The length of one diagonal is [tex]5\sqrt2\ in[/tex]
As there are 4 diagonals the sum of the lengths of the prism is [tex]4\times 5\sqrt2=20\sqrt5[/tex]
With the given information the exact dimensions of the prism cannot be determined as the two equations cannot be solved and trigonometry can also be not used.
