A rectangle is to be inscribed in a semicircle of radius 2, as shown in the figure. What i...

A rectangle is to be inscribed in a semicircle of radius 2, as shown in the figure. What is the largest possible area of such a rectangle? [Hint: The width of the rectangle is the second coordinate of the point P (why?), and P is on the top half of the circle x2 + y2 = 4.]