SOLUTION: A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width, equal to the area of the factory, must surround it. How wide is the strip of the lawn and what

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Question 909913: A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width, equal to the area of the factory, must surround it. How wide is the strip of the lawn and what are the dimensions of the factory? (Maybe something to do with using the quadratic formula or factoring?)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
80*60=4800 m^2
(80+x)*(60+x)=9600
x^2+140x+4800 = 9600
x^2+140x-4800 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B140x%2B-4800+=+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=%28140%29%5E2-4%2A1%2A-4800=38800.

Discriminant d=38800 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-140%2B-sqrt%28+38800+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28140%29%2Bsqrt%28+38800+%29%29%2F2%5C1+=+28.488578017961
x%5B2%5D+=+%28-%28140%29-sqrt%28+38800+%29%29%2F2%5C1+=+-168.488578017961

Quadratic expression 1x%5E2%2B140x%2B-4800 can be factored:
1x%5E2%2B140x%2B-4800+=+1%28x-28.488578017961%29%2A%28x--168.488578017961%29
Again, the answer is: 28.488578017961, -168.488578017961. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B140%2Ax%2B-4800+%29

x=28.489
(80+28.489)*(60+28.489)=9600
(108.489)*(88.489)=9600
108.489*88.489=9600.083121