#### Objectives

- Students will determine the relationship between the width and length of a garden with a rectangular shape and a fixed amount of fencing. The garden is attached to a barn, and exactly three sides of the garden will be fenced.
- Students will determine a formula that can be used to compute the area of the garden when given the width.
- Students will find the dimensions of the garden that has the maximum possible area.

#### Vocabulary

- perimeter
- area
- maximize
- conjecture

#### About the Lesson

In this activity, students explore the area of a garden with a rectangular shape that is attached to a barn. Exactly three sides of the garden must be fenced. Students will sketch possible gardens and enter their data into a spreadsheet.

As a result students will:

- Graph the data, find an equation for the area of the garden in terms of its width, find the maximum area of the garden, and solve related problems.
- Determine that, given a fixed perimeter, the area enclosed depends upon the dimensions chosen.

The extension problem provides an opportunity for students to explore a different scenario—a garden with a rectangular shape that must be fenced on all four sides. Problem 2 in the TI-Nspire™ document may be used to explore this scenario.