Question 1012985
sides are x and 16-x
They add to 16 which is half the perimeter.
square them to x^2 and (16-x)^2, and that equals D^2, where D is the diagonal.
x^2+256-32x+x^2=D^2
D^2=2x^2-32x+256
The minimum is the vertex and x=-b/2a at the vertex.  That is 32/4=8
The diagonal is shortest when the rectangle is a square, with sides 8.  The diagonal length squared is 128, so the diagonal is 8 sqrt(2), from a 45-45-90 right triangle.