Problem 3.1

Problem 3.1 The rangers in Great Smoky Mountains National Park want to build several inexpensive storm shelters. The shelters must have 24 square meters of floor space. Suppose that the walls are made of sections that are 1 meter wide and cost $125.

Part A Use your tiles to experiment with different rectangular shapes. Sketch each possible floor plan on grid paper. Record your group’s data in a table with these column headings: Length Width Perimeter Area Cost of Walls

Part B Based on the cost of the wall sections, which design would be the least expensive to build? Describe what that shelter would look like.

Part C Which shelter plan has the most expensive set of wall sections? Describe what that shelter would look like.

Follow-up Can you find a design-other than a rectangle- with 24 square meters of floor space and lower wall-section costs than any of the designs you have looked at so far? Experiment with your tiles to answer this question.