SOLUTION: A farmer plans to use 21 meters of fencing to enclose a rectangular pen having an area of 55 meters. Only three sides of the pen need fencing because parts of an existing wall wil

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Question 197244: A farmer plans to use 21 meters of fencing to enclose a rectangular pen having an area of 55 meters. Only three sides of the pen need fencing because parts of an existing wall will form the forth side. Find the dimensions of the pen?

PLEASE HELP I DONT UNDERSTAND!!!!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer plans to use 21 meters of fencing to enclose a rectangular pen having an area of 55 meters. Only three sides of the pen need fencing because parts of an existing wall will form the forth side. Find the dimensions of the pen?
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He'll use 21 meters to make 3 sides.
Call the length (L) the side parallel to the wall, and the other 2 sides the width (W).
21 = L + 2W
Area = L*W = 55
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L = 21 - 2W (from the 1st eqn)
(21-2W)*W = 55
2W^2 - 21W + 55 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-21x%2B55+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-21%29%5E2-4%2A2%2A55=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+1+%29%29%2F2%5C2+=+5.5
x%5B2%5D+=+%28-%28-21%29-sqrt%28+1+%29%29%2F2%5C2+=+5

Quadratic expression 2x%5E2%2B-21x%2B55 can be factored:
2x%5E2%2B-21x%2B55+=+%28x-5.5%29%2A%28x-5%29
Again, the answer is: 5.5, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-21%2Ax%2B55+%29

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W = 5, L = 11 or
W = 5.5, L = 10
either way will work