The following information is known about points A, B, C, D, and E in the plane.
$$\begin{aligned}
& { [ A B ] \perp [ B C ] } \\
& { [ A B ] \cap [ C D ] = E } \\
& | A E | = | B C | = 4 \text { units } \\
& | A B | = | C D | = 7 \text { units }
\end{aligned}$$
Given this, what is the length |DE| in units?\\
A) $\sqrt { 3 }$\\
B) $\sqrt { 5 }$\\
C) $\sqrt { 7 }$\\
D) 2\\
E) 3