SOLUTION: The length of the diagonal of a rectangle is shorter than the semi-perimeter by the length of the longer side. If the dimensions of all sides are integers, find the minimum length

This is an instructive problem, to get students to think outside the box.







Square both sides:







Substituting 

So the width can be any length.

So it is a rectangle which has degenerated into a line segment, 
its length.

Think of this:



Now think of it shrinking to this



Then to this:



Then to this:



Then to this:



Then to this:



The diagonals are approaching the lengths of the longest sides.

The shortest side is approaching 0 in which the rectangle will become 
a straight line.

This is an instructive problem.  To think of figures approaching other
shapes.

The minimum length of the shortest sides is 0.

Edwin