Lesson 6: Optimizing Areas and Perimeters

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Presentation transcript:

Lesson 6: Optimizing Areas and Perimeters LG: I can determine the maximum area. I can determine the minimum perimeter.

Maximum Area Among all rectangles with a given perimeter, a square has the maximum area. Example 1 What are the dimensions of a rectangle with a perimeter of 30 m that gives a maximum area?

Minimum Perimeter Among all rectangles with a given area, a square has the minimum perimeter. Example 2 What are the dimensions of a rectangle with an area of 45 m2 that gives a minimum perimeter?

Minimize Perimeter with Constraints A rectangular garden is to be fenced using the wall of a house as one side of the garden. The garden should have an area of 40 m2. Determine the minimum perimeter and dimensions of the garden (to whole numbers).

Rectangular or Circular? A hobby farmer is creating a fenced yard for her goats. She has 900 m of flexible fencing and wants to maximize the area. Determine whether a rectangular area or circular area creates the greater area?

Practice Questions Page 94 #1-3, 7, 12, 13