Question 3405
 Let the three sides be y, x and y 
 Sum of the three sides x + 2y = 80 , so y = (80-x)/2
 Area of the rectangle A = xy = x(80-x)/2 = 40x -x^2/2
 
 By complete square A = -1/2(x^2 - 80x + (80/2)^2) + 1600/2
  = -1/2(x - 40)^2 + 800
 Since (x - 40)^2 >=0,   -1/2(x - 40)^2 <= 0,
 A = -1/2(x - 40)^2 + 800 <= 800,
 when x = 40, y = (80-40)/2 = 20.

 Hence, when the dimensions of the field are 20,40 and 20 meters
  the max area is 800 sq. meters.


 Kenny
 PS. Also, try to get rid of some redunant words which are not
     related to math in this question. Like :
  There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle.