The respective length, breadth and height of the

**rectangular cuboid** R

_{1} is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R

_{2} is A, B and C.

It is known that:

(i) The volume of R

_{1} is precisely twice that of R

_{2}, and:

(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?) by Jer)

Jer:

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!