SOLUTION: A rectangle is 4 feet longer than it is wide and its area is 60 sqft. find it's dimensions?

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Question 147500: A rectangle is 4 feet longer than it is wide and its area is 60 sqft. find it's dimensions?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
L = W + 4
L*W = 60
W*(W+4) = 60
W%5E2+%2B+4W+=+60
W%5E2+%2B+4W+-+60+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-60+=+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=%284%29%5E2-4%2A1%2A-60=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%284%29-sqrt%28+256+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B4x%2B-60 can be factored:
1x%5E2%2B4x%2B-60+=+%28x-6%29%2A%28x--10%29
Again, the answer is: 6, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-60+%29

Since a negative width makes no sense, we go with W = 6.
That makes the length = 10.
BTW, it's means "it is", not "it is dimensions"