2024 AMC 12B Problem 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?

\textbf{(A) }909\qquad \textbf{(B) }910\qquad \textbf{(C) }911\qquad \textbf{(D) }912\qquad \textbf{(E) }913\qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.