Rectangle ABCD is inscribed in sqyare RSTU if the length of AC is k and the length os CD is m, what is the length of a side of square RSTU in terms of k and m

Question

anonymous · Answer

anything could be the area because it is not told whether any of this two side is the base or not

anonymous · Answer

I'm not trying to find area

kfujioka · Answer

There's only a couple ways to inscribe a rectangle in a square.  The first is trivial, but indeterminate where k and m are drawn parallel to the square's side, then either k or m will be the length of a side.  In the nontrivial case, k and m must be parallel to the square's diagonals and there's 90 and 45 degree angles all over the place.
If you look along one diagonal of length S*sqrt(2), you should see that it's length is k+m.  So the length of the square's side S is:$$[\sqrt2(k+m)]/2$$