When does it have maximum area?

Problem. Let ABC be a triangle in which ∡B and ∡C are acute, and let PQRS be a rectangle inscribed in the triangle, with vertex P on side AB, vertices Q and R on side BC, and vertex S on side AC. Find the maximum possible value of the ratio of the area of rectangle PQRS to that of triangle ABC. Obviously, infinitely many possibilities exist for the inscribed rectangle, as Figure 1 suggests. Which of them has maximum area