calculus optimization problem

[thegame]

What is the area of the largest rectangle that can be inscribes indiside a semicircle with the radius r?

answer: x = r / SQRT(2)
A = r^2

[gnome]

Is there a question here?

[thegame]

How do you ge the answer?

[gnome]

How did YOU get the answer?

[Hurkyl]

Well, if you know one side of a rectangle inscribed in a semicircle, can you figure out the other side?

[gnome]

What Hurkyl's getting at is:

Draw the semicircle. Draw a rectangle inside it, call one side h, call the other side w, call the radius r.

Now find a relationship that lets you eliminate either h or w. In other words, express h as a function of w, or w as a function of h.