The perimeter of a rectangle in units equals its area in units squared. (4,4), (3,6), and (6,3) are three possible pairs of lengths for this rectangle.

Give another pair of positive integral sides for this rectangle or prove why there isn't another pair.

I could have said that there is no other pair quite soon after trying a couple values.
None of the sides can be smaller than 3, because 2*y = 2(2+y) <=> 2y = 4+2y -> 0 = 4
which is false.
After trying values larger than 3 you notice very soon that the function (if you had drawn a graph) blows up. The area becomes too large for the perimeter to keep up with.
It's a solution without elegance, but there are at least some useful thoughts in the beginning. ;)

Posted by abc on 2003-09-12 19:57:51