The respective length, breadth and height of the rectangular cuboid
is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R2
is A, B and C.
It is known that:
(i) The volume of R1
is precisely twice that of R2
(ii) Each of A, B and C is a positive integer with A ≤ B ≤ C
Determine the maximum value of C.
(In reply to Probable solution (is my reasoning sensible?)
I don't think your reasoning is quite right, but I think you came up with the right answer.
In order to maximize C, we want
(A+2)(B+2)/AB to be as large as possible but still under 2.
If A = 3 and B = 11, then (A+2)(B+2)/AB ~ 1.97
It is quite clear from your work that A and B must both be between 3 and 11. Seems like there is still room for improvement, but a quick excel check didn't find anything better.
If A = B = 5, then (A+2)(B+2)/AB is only 1.96
If A = 4 and B = 7 then (A+2)(B+2)/AB is only ~ 1.93
So, I like your answer!