Maximizing a Triangle

5.4.1: Maximizing a Triangle A new medical center has just been built and it Is ready for landscaping. The owners of the building want to put in a triangular planting area between the front sidewalk \"9'1\"" Building and the walk leading up to the building. They have enough solar lights to go around 15 m of garden. The lights will go around all three sides of the garden. As the landscaper you need to determine the lengths of the sides of the triangle that will maximize the planting area for the garden. "a! Investigate Open Geometer's SketchPad and use the provided sketch to complete the table on the back of the sheet as follows: 0 Create at least 10 different triangles and record their information in the table. Remember, you are looking for the triangle with the greatest area. 0 Include a sketch of each triangle in the last column. Your sketch does not have to be exact, but should be a good representation of the triangle (i.e. it should show which side is longer. a or b) Make sure all of your triangles have a perimeter of 15 m. Conclusions When you have completed the chart. answer the following questions: 1. Which triangle had the greatest area? 2. is there anything special about this triangle? 3. Give a hypothesis for how to maximize the area of any n'g ht triangle with a given perimeter