SOLUTION: A rectangular storage area is 8.0 meter longer than it is wide. If the area is 28m^2, what are its dimensions?

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Question 437160: A rectangular storage area is 8.0 meter longer than it is wide. If the area is 28m^2, what are its dimensions?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Area = Length * Width
A = L*W
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We're told
A = 28
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We're also told the length is 8 meters greater than width.
L = W+8
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L * W = A
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Substituting:
(W+8) * W = 28
W^2 + 8W = 28
Subtract 28 from both sides
W^2 + 8W - 28 = 0
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This does not factor easily, so use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B8W%2B-28+=+0) has the following solutons:

W%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=%288%29%5E2-4%2A1%2A-28=176.

Discriminant d=176 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+176+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%288%29%2Bsqrt%28+176+%29%29%2F2%5C1+=+2.6332495807108
W%5B2%5D+=+%28-%288%29-sqrt%28+176+%29%29%2F2%5C1+=+-10.6332495807108

Quadratic expression 1W%5E2%2B8W%2B-28 can be factored:
1W%5E2%2B8W%2B-28+=+1%28W-2.6332495807108%29%2A%28W--10.6332495807108%29
Again, the answer is: 2.6332495807108, -10.6332495807108. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-28+%29

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A negative value for W does not make sense, so we choose W = 2.633.
L = W + 8 = 10.633.
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Checking.
10.633*2.633=27.9966 or about 28.
.
Done.