Answer: Option C
Sum of perimeters of the six faces :
$$\eqalign{
& = 2\left[ {2\left( {l + b} \right) + 2\left( {b + h} \right) + 2\left( {l + h} \right)} \right] \cr
& = 4\left( {2l + 2b + 2h} \right) \cr
& = 8\left( {l + b + h} \right) \cr} $$
Total surface area $$ = 2\left( {lb + bh + lh} \right)$$
$$\eqalign{
& \therefore 8\left( {l + b + h} \right) = 72 \cr
& \Rightarrow l + b + h = 9 \cr
& 2\left( {lb + bh + lh} \right) = 16 \cr
& \Rightarrow lb + bh + lh = 8 \cr} $$
Now,
$${\left( {l + b + h} \right)^2} = {l^2} + {b^2} + {h^2} + 2$$     $$\left( {lb + bh + lh} \right)$$
$$\eqalign{
& \Rightarrow {\left( 9 \right)^2} = {l^2} + {b^2} + {h^2} + 16 \cr
& \Rightarrow {l^2} + {b^2} + {h^2} = 81 - 16 \cr
& \Rightarrow {l^2} + {b^2} + {h^2} = 65 \cr} $$
Required length :
$$\eqalign{
& = \sqrt {{l^2} + {b^2} + {h^2}} \cr
& = \sqrt {65} \cr
& = 8.05\,cm \cr} $$