Question 1675
 Let te dimensions of the rectangles be x,y.
 Since the perimeter is 2(x+y)= 20,so x+y = 10.

 The area A = xy = x(10-x) = -x^2 + 10x
   (by complete square)
            = -(x^2 - 10x + 25) + 25
            = -(x - 5)^2 + 25
   (since -(x - 5)^2  <= 0 for all x)
   A has max value if x =5 and so y = 10-5 =5.
 
 Hence, when the rectangle dimensions are 5, 5 , its area is max.

 Also, note that in this case, Area/perimeter = 25/20 = 1.25

 If the shape is a circle, then we see that
  Area/perimeter = (pi R^2)/(2pi R) = R/2
 Therefore, when the radius R > 2.5 , the circle is more efficient 
 than the rectangle. (higher area to perimeter ratio)


 Kenny