Question

Find the dimensions of largest rectangle w/ maximum area inscribed in a semicircle with radius r.
What equations am I gonna use in here? Help!

Answer 1

put the semicircle with center at the origin

Answer 2

then the equation for the circle is \(x^2+y^2=r^2\) which means \(y=\sqrt{r^2-x^2}\)
a point on the circle will look like \((x, \sqrt{r^2-x^2})\)