Square $ABCD$ has side length $10$. Point $E$ is on $\overline{BC}$, and the area of $\bigtriangleup ABE$ is $40$. What is $BE$?

$\textbf{(A)} \ 4 \qquad \textbf{(B)} \ 5 \qquad \textbf{(C)} \ 6 \qquad \textbf{(D)} \ 7 \qquad \textbf{(E)} \ 8 \qquad$
We are given that the area of $\triangle ABE$ is $40$, and that $AB = 10$.
The area of a triangle is:
$A = \frac{bh}{2}$
Using $AB$ as the height of $\triangle ABE$,
$40 = \frac{10b}{2}$
and solving for $b$,
$b = 8$, which is $\boxed{\textbf{(E)}}$