Brooklyn has 24m of fencing. She wants to build a rectangualr enclosure for her dog with the maximum possible area.

Question

Write a function to represent the rectangular area of the enclosure. How do you know that the function is quadratic?

Answer 1

 

  Perimeter P = 2*L + 2* w

 

             24 = 2*L + 2* w

 

            12 = L + w

 

            L = 12 - w

 

 Area A = L * w

 

 Area A = (12 - w)* w

 

           = 12*W - w^2

 

It is quadratic because of the w^2

 

The max occurs at the AVERAGE of the zeros.

The zeros are 0 = 12w - w^2

                     0 = (12 - w)w

              w = 0 or 12-w = 0

             w = 0 or 12 = w

 

   The  average is (0 + 12)/2 = 12/2 = 6

 

The length is also 12-6 = 6

 

The max area is 36.