Question 18
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 $BC$. 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 $p + q + r + s$?
(A) 909 (B) 910 (C) 911 (D) 912 (E) 913
(A) 909 (B) 910 (C) 911 (D) 912 (E) 913