Fence Problem 1

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

• 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.

Make a Prediction: Determine the dimensions of the field that will enclose the largest area. What shape is this field?

• Check your predictions by changing the dimensions of the field until the calculated area is the greatest.

Make a Prediction: Determine the dimensions of the field that will enclose the smallest area. What shape is this field?

• Check your predictions by changing the dimensions of the field until the calculated area is the smallest.

Elaboration: What is the domain for this problem? That is, what are the possible values for the width of the field? What is the range for this problem? That is, what are the possible values for the height of the field? Write an equation for the amount of fence the farmer has (this is your constraint). Write an equation for the area of the field (this is what your are maximizing or minimizing).