Local extrema

Imagine you have a house with a backyard in the shape of a semicircle, but you're not really using it for anything. It gets plenty of sunlight, so you decide to install a solar panel. However, your local manufacturer only makes rectangular solar panels. What is the maximum area your solar panel can have, knowing that the radius of the semicircle is $30\sqrt2$ meters? Enter only numbers, the unit is not required.

Remember:

• A semicircle can be described as: $y = \sqrt{r^2 - x^2}$
• $A_{rectangle} = base \cdot height$

Tip: If we set the origin of coordinates at the center of the circle, we can see that the base of our rectangle is: $base=2x$ since the semicircle is symmetric about the y-axis, and its height is: $height = y$