Question

Maximum Area: Kevin wants to fence a garden using 14 rails of 8-foot each that he can't cut. What are the dimensions of the rectangle that will maximize the fenced area?

The answer is NOT 28ft by 28ft because we can’t cut the rails. It needs to be made by whole rails of 8 feet each.

Answer 1

To make the maximum area, there should be a minimum difference between the height and length of the rectangle.
14 rails make the total perimeter of the rectangular garden.
The perimeter of the rectangle = 2( a + b) :: Where a and b are height and length respectively.  
2(a + b ) = 14
a + b = 7 : 7 can be written as 3 + 4, 2 + 5, 1 + 6, but the minimum difference in 3 and 4
a + b = 3 + 4
a = 3 Rails = 24 foot
b = 4 Rails = 32 foot
So, the diamention of rectangular garden is 24ft by 32ft
Area in that case = 768 ft square