Optimization: Wire Problem 2

Author:
hpp3
A 12 foot piece of wire is cut into two pieces and one piece is bent into a square and the other piece is bent into an equilateral triangle. Determine where to cut the wire so that the area enclosed by the two shapes is a maximum or a minimum.
Instructions:
  • Drag the "Where to Cut" slider to change where the wire is cut and see how the dimensions of the two shapes change.
Make a prediction: Where should the wire be cut so that the total area enclosed by both shapes is a maximum? Explain.
  • Click the Check Box "Show Areas" to see the area of each object. Again, use the slider or drag the triangular marker to change where the wire is cut and see how the areas of the two shapes change. Also notice how the total area changes. Was your prediction correct? Why or why not?
Make a prediction: Where should the wire be cut so that the total area enclosed by both shapes is a minimum? Explain.
  • Click the Check Box "Show Areas" to see the area of each object. Again, use the slider or drag the triangular marker to change where the wire is cut and see how the areas of the two shapes change. Also notice how the total area changes. Was your prediction correct? Why or why not?