SOLUTION: The length of a rectangular backyard is 8 meters longer than the width. If the are is equal to 92 square meters, what are the dimensions of the backyard? Round to the nearest thous

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Question 986128: The length of a rectangular backyard is 8 meters longer than the width. If the are is equal to 92 square meters, what are the dimensions of the backyard? Round to the nearest thousandth. [only an algebraic solution will be accepted.]
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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L=length; W=width=L-8m; A=area=92m^2
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A=%28L%29%28W%29
92m%5E2=%28L%29%28L-8m%29
92m%5E2=L%5E2-8L
0=L%5E2-8L-92
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-92+=+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=%28-8%29%5E2-4%2A1%2A-92=432.

Discriminant d=432 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+432+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+432+%29%29%2F2%5C1+=+14.3923048454133
x%5B2%5D+=+%28-%28-8%29-sqrt%28+432+%29%29%2F2%5C1+=+-6.39230484541326

Quadratic expression 1x%5E2%2B-8x%2B-92 can be factored:
1x%5E2%2B-8x%2B-92+=+1%28x-14.3923048454133%29%2A%28x--6.39230484541326%29
Again, the answer is: 14.3923048454133, -6.39230484541326. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-92+%29

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L=14.392m ANSWER 1: The length is 14.392 meters.
W=L-8=14.392-8=6.392m ANSWER 2: The width is 6.392 meters.