Answer:
50 ft by 33 1/3 ft
Step-by-step explanation:
Let x represent the dimension perpendicular to the shared fence. Then the dimension parallel to the shared fence will be ...
y = (200-2x)/3
The area will be the product of these dimensions, so will be ...
area = xy = x(200 -2x)/3 = (2/3)x(100 -x)
area = (-2/3)(x^2 -100x)
To complete the square, we need to add the square of half the x-coefficient inside parentheses, and the opposite of that quantity outside parentheses.
area = (-2/3)(x^2 -100x +2500) +(2/3)(2500) . . . . complete the square
area = (-2/3)(x -50)^2 + 5000/3
The vertex of this parabolic curve is at x=50, so the dimensions of the maximum area are ...
x = 50 . . . feet
y = (200 -2·50)/3 = 33 1/3 . . . feet
