In [quadrilateral](https://artofproblemsolving.com/wiki/index.php/Quadrilateral) $ABCD$, $\angle B$ is a [right angle](https://artofproblemsolving.com/wiki/index.php/Right_angle), [diagonal](https://artofproblemsolving.com/wiki/index.php/Diagonal) $\overline{AC}$ is [perpendicular](https://artofproblemsolving.com/wiki/index.php/Perpendicular) to $\overline{CD}$, $AB=18$, $BC=21$, and $CD=14$. Find the [perimeter](https://artofproblemsolving.com/wiki/index.php/Perimeter) of $ABCD$.
From the problem statement, we construct the following diagram: 


Using the [Pythagorean Theorem](https://artofproblemsolving.com/wiki/index.php/Pythagorean_Theorem):

$(AD)^2 = (AC)^2 + (CD)^2$
$(AC)^2 = (AB)^2 + (BC)^2$
Substituting $(AB)^2 + (BC)^2$ for $(AC)^2$: 

$(AD)^2 = (AB)^2 + (BC)^2 + (CD)^2$
Plugging in the given information: 

$(AD)^2 = (18)^2 + (21)^2 + (14)^2$
$(AD)^2 = 961$
$(AD)= 31$
So the perimeter is $18+21+14+31=84$, and the answer is $\boxed{084}$.