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Question 419217: A farmer has 300 yards of fencing and wants to enclose a rectangular area of 5600 square yards what dimensions should he use?
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! 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.
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