What is the ratio of the width to length of a folded sheet of paper if the rectangle formed when the sheet is folded in half (as shown below) is similar to the original rectangular sheet? Express your answer as a common fraction in simplest radical form. (Assume the width of the original sheet of paper becomes the length of the folded sheet.) [asy] pair A =(0,0), B=(4,0), C=(4,5), D = (0,5); draw(A--B--C--D--A); pair F = (3,6), G = (3,5), H = (3,1); draw(D--F--G); draw(G--H--A,dotted); label("width",midpoint(A--B),S); label("length",midpoint(A--D),W); [/asy]
