SOLUTION: The perimeter of a rectangular field is 60 meters. Its area is 2, square meters. What are its dimensions? Thank you!

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Question 893389: The perimeter of a rectangular field is 60 meters. Its area is 2, square meters. What are its dimensions?
Thank you!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangular field is 60 meters. Its area is 2, square meters. What are its dimensions?
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2L + 2W = 60
L*W = 2 --> L = 2/W
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L + W = 30
2/W + W = 30
2 + W^2 = 30W
W^2 - 30W + 2 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-30x%2B2+=+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=%28-30%29%5E2-4%2A1%2A2=892.

Discriminant d=892 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--30%2B-sqrt%28+892+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+892+%29%29%2F2%5C1+=+29.9331845230681
x%5B2%5D+=+%28-%28-30%29-sqrt%28+892+%29%29%2F2%5C1+=+0.0668154769319216

Quadratic expression 1x%5E2%2B-30x%2B2 can be factored:
1x%5E2%2B-30x%2B2+=+%28x-29.9331845230681%29%2A%28x-0.0668154769319216%29
Again, the answer is: 29.9331845230681, 0.0668154769319216. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-30%2Ax%2B2+%29

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W = 0.0668154769319216 m
L = 29.9331845230681 m