amc-2014-im-18

Two rectangular prisms are constructed.

One measures 4cm \(\times %speech% ,by,\) 6cm \(\times %speech% ,by,\) \(x\,\)cm and the other measures 3cm \(\times %speech% ,by,\) 8cm \(\times %speech% ,by,\) \(y\,\)cm, where both \(x\) and \(y\) are integers.

If they have equal surface area, what is the smallest possible value of \(x+y %speech% ,x+y,\)?