A farmer needs to enclose a field with a fence. She has 10 meters of fencing material. Determine the dimensions of the field that will enclose the largest and smallest areas.
Instructions: [list][*]Drag the purple 'X' or use the 'Show Animation' and 'Stop Animation' Buttons to change the dimensions of the field. [*]Click the check box 'Show Area' to show or hide the calculated area. [/list] [i]Make a Prediction[/i]: Determine the dimensions of the field that will enclose the largest area. What shape is this field? [list][*]Check your predictions by changing the dimensions of the field until the calculated area is the greatest.[/list] [i]Make a Prediction[/i]: Determine the dimensions of the field that will enclose the smallest area. What shape is this field? [list][*]Check your predictions by changing the dimensions of the field until the calculated area is the smallest.[/list] Elaboration: [list][*]What is the domain for this problem? That is, what are the possible values for the [i]width[/i] of the field? [*]What is the range for this problem? That is, what are the possible values for the [i]height[/i] of the field? [*]Write an equation for the amount of fence the farmer has (this is your [i]constraint[/i]). [*]Write an equation for the area of the field (this is what your are [i]maximizing[/i] or [i]minimizing[/i]). [/list]