Question 419217
Let x = width of the rectangle
Let y = length of the rectangle

Since the total amount of fencing is 300 yards, the perimeter of the rectangle must be 300.  Perimeter is the sum of all of the sides, that is x + y + x + y.  So, we have:

2x + 2y = 300

We also know that the area (length times width) is 5600.  So we have:

xy = 5600

From the first equation, we know that:
2x + 2y = 300
x + y = 150 (dividing both sides by 2)
x = 150 - y (subtracting y from both sides)

We can make the substitution in the "area" equation:
xy = 5600
(150 - y)y = 5600 (substituting the expression from above for x)
150y - y^2 = 5600
y^2 - 150y + 5600 = 0 (rearranging terms and establishing a quadratic equation)
(y - 70)(y - 80) = 0 (factoring)
y = 70 or y = 80

If y = 70, then x = 80
If y = 80, then x = 70

So, the dimension of the fenced in area is 70 by 80.