### Instruction: In quadrilateral $ABCD$, $\angle B$ is a right angle, diagonal $\overline{AC}$ is perpendicular to $\overline{CD}$, $AB=18$, $BC=21$, and $CD=14$. Find the perimeter of $ABCD$.### Response: I notice that the quadrilateral has two right triangles, $\triangle ABC$ and $\triangle ACD$, so I can use the Pythagorean theorem to find some missing lengths.
First, I use the Pythagorean theorem on $\triangle ABC$ to find $AC$.
I have $AC^2=AB^2+BC^2$, so $AC^2=18^2+21^2=324+441=765$.
Taking the square root of both sides, I get $AC=\sqrt{765}$.
Next, I use the Pythagorean theorem on $\triangle ACD$ to find $AD$.
I have $AD^2=AC^2+CD^2$, so $AD^2=765+14^2=765+196=961$.
Taking the square root of both sides, I get $AD=31$.
Now I have all the side lengths of the quadrilateral: $AB=18$, $BC=21$, $CD=14$, and $AD=31$.
To find the perimeter, I just add them up: $18+21+14+31=84$.