Maximizing the area of a rectangle inscribed in a 3-4-5 triangle

A rectangle is inscribed in a 3-4-5 right triangle as shown below. Drag the [color=#ff00ff][b]pink point[/b][/color] to change the dimensions of the rectangle.[br][br]What dimensions maximize the area of this rectangle?[br]What is the maximum area of this rectangle?
[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]
– Tim Brzezinski

Information: Maximizing the area of a rectangle inscribed in a 3-4-5 triangle