2.6 Optimizing Perimeter & Area

When enclosing a rectangular area on 4 sides, the maximum area occurs when

• The length is much longer than the width

• The length is slightly longer than the width

• The length is shorter than the width

• The length is equal to the width

When enclosing a rectangular area on 3 sides, the maximum area occurs when

• the length is equal to the width

• the length is twice the width

• the length is triple the width

• the length is half the width

If you have 100 m of fencing to enclose an area with 4 sides, how long should each side length be in order to maximize the area?

• Length = 25 m

  Width = 25 m

• Length = 30 m

  Width = 20 m

• Length = 40 m

  Width = 10 m

• Length = 35 m

  Width = 15 m

If you have 130 m of fencing to enclose an area with 4 sides, how long should each side length be in order to maximize the area?

• Length = 32.5 m

  Width = 32.5 m

• Length = 40 m

  Width = 25 m

• Length = 50 m

  Width = 15 m

• Length = 30 m

  Width = 30 m

If you have 210 ft. of fencing to enclose an area around 3 sides, how long should each side be to have a maximum area?

• Length = 70 ft.

  Width = 70 ft.

• Length = 105 ft.

  Width = 52.2 ft.

• Length = 100 ft.

  Width = 55 ft.

• Length = 90 ft.

  Width = 45 ft.

A rectangular yard is fenced on 4 sides and has an area of 170 square feet. How long should its sides be to minimize fencing?

• 10 ft.

• 13 ft.

• 40 ft.

• 85 ft.

A rectangular garden has an area of 25 square meters and is enclosed on 4 sides. How long should its sides be to minimize fencing?

• 5 m

• 7 m

• 12.5 m

• 6.25 m