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.
I started by trying to find solutions with c=1 and c=2 (there are none).
When c=3 the equation becomes
(A+2)(B+2)*5=2AB*3
or
B  (10A+20)/(A10)
the first solution is A=11, B=130, C=3
Then I realized that due to the symmetry of this situation there is a solution when C=130.
Then I realized that the other two values are minimized and the third is maximized.
So the maximum value of C is 130.
(Does this reasoning work?)

Posted by Jer
on 20141105 22:36:58 