Suppose a square piece of paper is folded in half vertically.  The folded paper is then cut in half along the dashed line.  Three rectangles are formed-a large one and two small ones.  What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
$\text{(A)}\ \frac{1}{2} \qquad \text{(B)}\ \frac{2}{3} \qquad \text{(C)}\ \frac{3}{4} \qquad \text{(D)}\ \frac{4}{5} \qquad \text{(E)}\ \frac{5}{6}$
[asy] draw((0,0)--(0,8)--(6,8)--(6,0)--cycle); draw((0,8)--(5,9)--(5,8)); draw((3,-1.5)--(3,10.3),dashed); draw((0,5.5)..(-.75,4.75)..(0,4)); draw((0,4)--(1.5,4),EndArrow); [/asy]
From here on, a blue line represents a cut, the dashed line represents the fold.

From the diagram, we can tell the [perimeter](https://artofproblemsolving.com/wiki/index.php/Perimeter) of one of the small rectangles is $2(4x+x)=10x$ and the perimeter of the large [rectangle](https://artofproblemsolving.com/wiki/index.php/Rectangle) is $2(4x+2x)=12x$.  The desired [ratio](https://artofproblemsolving.com/wiki/index.php/Ratio) is \[\frac{10x}{12x}=5/6\rightarrow \boxed{\text{E}}\]