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Optimal Design for a Rectangular Dog Pen with 24 Meters of Fencing

Help your friend build the perfect rectangular dog pen for Shane using 24 meters of fencing. This project explores different rectangular shapes that can be formed with the available fencing. By experimenting with square tiles, sketch various rectangles that have a perimeter of 24 meters. Record your findings in a table including Length, Width, Perimeter, and Area. Discuss which design offers the best space for Shane to run and play, ensuring a comfortable and enjoyable environment for her dog.

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Optimal Design for a Rectangular Dog Pen with 24 Meters of Fencing

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  1. Problem 4.1 • Suppose you wanted to help a friend build a rectangular pen for her dog, Shane. You have 24 meters of fencing, in 1-meter lengths, to build the pen. Which rectangular shape would be the best for Shane?

  2. Problem 4.1 • Experiment with your square tiles to find all possible rectangles with a perimeter of 24 meters. Sketch each rectangle on grid paper. Record your data about each possible plan in a table with these column headings: • Length, Width, Perimeter, and Area

  3. Follow-up • Which design would give Shane the best pen for running? • Which design would give Shane the most space for playing?

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