Solve This!

Pens I

Farmer Mead has 36 Guinea pigs on her farm. She wants to build one rectangular pen for them and must allow one square meter of area for each Guinea pig. The fencing material costs one dollar per meter. Farmer Mead wants to build the least expensive pen that will hold all 36 pigs. Can you help her find it?

• On graph paper draw all the possible rectangles using whole dimensions. Hint: think of factors of 36. Label the dimensions and calculate the cost of the fence for each rectangle. Hint: the perimeter number is the cost and it is the sum of the four sides.
  
  
• Create a table to organize your data. Show the dimenions and cost of each rectangle.
  
  

  You may extend your project by doing one or both of these:
  

  Use a computer spreadsheet to create your table.
  

  Investigate similar pens using other areas.

  Click Here to get the solution.

Sir Isaac Newton invented calculus to solve problems such as this. Click here to read about his life.

Click here to see a second version of the Pens problem called Pens II.