Optimization: Area of a Rectangle

Problem Taken from [i]Calclulus: Early Trancendentals[/i] (Thomas' 13th edition) - pg. 266: [br][br][i][color=#0000ff]A rectangle is to be inscribed in a semicircle of radius 2. What is the largest area the rectangle can have, and what are its dimensions? [/color][/i]

Information: Optimization: Area of a Rectangle