Expert: Sherry Wallin - 5/4/2010

Question
A dog owner wishes to enclose a rectangular area in his backyard for the dog. The owner wishes to use existing fencing along two adjacent sides of the rectangle and had 14 meters of new fencing available for the other two sides. suppose that we let the dimensions of the area be A m^2.
a) explain why x+y=14
b) explain why A = x(14 - x)

c)with a on the vertical axis and x on the horizontal axis make a sketch of a - x(14-x)
d) what is the greatest rectangular area the owner can enclose and what would be the dimensions that give this greatest area

Answer
Nick~
   The reason that x + y = 14 is because you have two unknown measurements and 14 meters of material.
  
   x + y = 14 then y = 14 - x. Area of a rectangle is length times width. Here one of either the length or the width is x and the other is y but y = 14-x so the area is lw = x(14-x).

   Sorry, I can't do the graph for you, no way to show it to you...

   the greatest rectangle in area is always a square. Since there is 14m to be used, let each side be 7 so that the area is 7^2 = 49 m^2

Math Prof