Me?
I'd cut the square extra large, like 7.5".
Cut it in half diagonally once.
Then place it on the rectangle by lining up one side,
and estimating the seam allowance.
Sew and press the triangle back.
It will overhand the edges of the rectangle.
Re-square/trim that end of the rectangle.
Do you resquare a rectangle, or rerectangle a retangle?
See what you did to me. ;) ;) ;) ;)
This doesn't create a lot of wasted fabric,
but it will guarantee that you'd still have the correct
measurement to use when attaching this unit to others.
If you're starting with a rectangle that's already cut
(iow, end is already at a 45 degree angle),
you can use the same triangle above.
If you want the exact measurement,
then it would be the 6 3/8 from the post upthread. ;-)
You're essentially creating a HST block on the end of
the rectangle.
However, if there's anything off in the cutting,
or the sewing, or the pressing, then when
you turn the triangle back, you won't have a perfect rectangle.
That's why I prefer the oversized method.
The 7.5" is just a number I picked that was bigger than the 6 3/8". ;) ;)