See the coversheet for instructions and the point value of each problem.

- Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius \(r\).
- A piece of wire \(10 \, \mathrm{m}\) long is
cut into two pieces. One piece is bent into a square and the
other is bent into an equilateral triangle.
- How should the wire be cut so that the total area enclosed is a maximum?
- How should the wire be cut so that the total area enclosed is a minimum?

- A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is \(30\, \mathrm{ft}\), find the dimensions of the window so that the greatest possible amount of light is admitted.

Last modified: Thu Nov 2 14:38:21 UTC 2017