maximum area?

Question

a stonemason has enough stones to enclose a rectangular patio with 60ft of stone wall. If the house forms one side of the rectangle, what should the dimensions of the patio in order to yield the maximum area?

Answer 1

Let x = length of the side parallel to the side of the house bordering the patio

     y = length of each of the other two sides

 

Then, x + 2y = 60.  So, x = 60-2y

 

Area = xy = (60-2y)(y)

 

               = -2y² + 60y

 

Maximum area when y = -60/[2(-2)] = 15 ft

 

                              x = 60-2y = 30 ft