Maribel is building a rectangular pen for her two dogs. She has 180 feet of fencing. She wants put fencing down middle to split the large rectangle in two

Question

What are the dimensions and area of the largest pen area she can use to accommodate both dogs?

Answer 1

If this is a calculus problem, once you have modeled the area in terms of x, take the derivative and find your critical point. This would be similar to finding the x value of the maximum of the curve.

Answer 2

Length of fence = 3x+2y = 180   (3 sides of length x and 2 sides of                                                                                    length y)

 

                  So, y = (180-3x)/2

 

Area = xy = x(180-3x)/2

 

               = (-3/2)x² + 90x

 

The graph of the area function is a parabola opening downward.  The graph has maximum when x = -90/[2(-3/2)]

       

                                        = -90/(-3) = 30

 

                                     y = (180-3x)/2 = 45

 

Build the pen with three parallel sides of length 30 ft and two parallel sides of length 45 ft.  The area of the entire pen is (30)(45) = 1350 ft² which is subdivided into two smaller pens, each with area 675 ft².