Section 12.8: Activity 12S
Draw at least two rectangles that have a perimeter of 20 units. Be sure at least one of your rectangles has side lengths that aren't whole numbers of units. Find the area of each of your rectangles.
If helpful, I have included the Segment of a Given Length tool, which will help you draw a segment with a specific length.
Question 1
As a class, we created a table listing rectangles with a perimeter of 20 units in order of decreasing area. What relationship does the dimension of the rectangles have with their area? What type of rectangle has the largest area?
Question 2
What if we opened our exploration up to shapes other than just rectangles? Given a specific perimeter, how do you think you would you find the shape with the largest area?
Question 3
Given your answer to Question 2, consider the following: A farmer has barbed wire he would like to enclose around his chicken coop. He has 40 feet of barbed wire. In order to have the biggest chicken coop, what shape should it be? What is the maximum area of the largest chicken coop he can enclose?