Question 20
Suppose $A,$ $B,$ and $C$ are points in the plane with $AB = 40$ and $AC = 42,$ and let $x$ be the length of the line segment from $A$ to the midpoint of $\overline{BC}.$ Define a function $f$ by letting $f(x)$ be the area of $\triangle ABC.$ Then the domain of $f$ is an open interval $(p, q),$ and the maximum value $r$ of $f(x)$ occurs at $x = s.$ What is $p + q + r + s?$