A rectangular piece of paper whose length is $\sqrt3$ times the width has area $\mathcal A$. The paper is divided into three equal sections along the opposite lengths, and then a dotted line is drawn from the first divider to the second divider on the opposite side as shown. The paper is then folded flat along this dotted line to create a new shape with area $\mathcal B$. What is the ratio $\mathcal B:\mathcal A$? $\textbf{(A)}\ 1:2\qquad$ $\textbf{(B)}\ 3:5\qquad$ $\textbf{(C)}\ 2:3\qquad$ $\textbf{(D)}\ 3:4\qquad$ $\textbf{(E)}\ 4:5$