SOLUTION: A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides. If the side parallel to the barn is to be twice the lengt

Click here to see ALL problems on Quadratic Equations

Question 705795: A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides. If the side parallel to the barn is to be twice the length of an adjacent side, and the area of the region is to be 162 ft2, how many feet of fencing should be purchased?
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
Since the region to be enclosed is rectangular we know its area will be length times width (or base times height). If we call the width "x", then the length will be "2x" (since we are told it is twice the length of the width).
We are also told that the area is to be 162 square feet. So the equation we can use is:

Now we solve for x. First we simplify:

Dividing both sides by 2:

Subtracting 81:

Factoring:
(x+9)(x-9) = 0
Using the Zero Product Property we get:
x+9 = 0 or x-9 = 0
Solving these:
x = -9 or x = 9

Since x represents the width of the region, we will discard the negative solution. (We are not interested in negatives sides of a region.) This makes 9 the only useable value for x (which is the width). And the length will be twice as much: 18.

Finally we answer the question: How much fencing should be purchased? Since the barn will serve as one side of the region we will no need fence for that side. We only need fencing for 1 length and 2 widths:
18 + 2*9 = 18 + 18 = 36 feet of fencing will be required.