The sum of the circumferences of two circles is \(\quantity{60\pi}{cm.}\) and the sum of their areas is \(\quantity{458\pi}{sq.cm.}\) Calculate the radii of the circles.

The radius of the red circle is \(r\) and the circumferences of the two circles add to \(60\pi\).

The rectangles have the same areas as the circles.

How many solutions are there?

What radius gives the minimum or maximum area?