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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

Question 841274: 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 648 ft squared, how many feet of fencing should be purchased?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x along the barn, y the dimension perpendicular to it.

y is also "the adjascent side" to the barn side.

the side parallel to the barn is to be twice the length of an adjacent side,x=2y;

Also described area, x%2Ay=%282y%29y=648

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Solving using algebra steps:
2y%5E2=648
y%5E2=324
y=sqrt%284%2A81%29
highlight%28y=18%29
-Find x using this value,
x=2y=2*18
highlight%28x=36%29
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Total fence length, the barn side takes care of one piece of fencing as itself, so the amount of fence material to buy would be highlight_green%28x%2B2y%29.
-------highlight%2872%29.