Question 253415
let length be l, width be w, and diagonal be d
let l be x, then w will be:
(8√2-2x)/2 = 4√2-x 
d^2=l^2+w^2
=x^2+(4√2-x)^2
=x^2+(32-8√2x-x^2) ___ not quite ___ the x^2 in the expansion is positive (negative times negative is positive)
=32-8√2x... ___ 2x^2 - 8√2x + 32


this is a quadratic (parabola) with a minimum on the axis of symmetry


x = -b / 2a = 8√2 / 4 = 2√2


substituting ___ d^2 = 2(2√2)^2 - 8√2(2√2) + 32 = 16 - 32 + 32 = 16


d = 4