SOLUTION: A rectangular skating rink measures 30 m by 14 m. It is to be doubled in area by extending each side by the same amount. Determine how much each side should be extended,

Algebra ->  Linear-equations -> SOLUTION: A rectangular skating rink measures 30 m by 14 m. It is to be doubled in area by extending each side by the same amount. Determine how much each side should be extended,      Log On


   

Question 988940: A rectangular skating rink measures 30 m by 14 m. It is to be doubled in area by extending each side by the same amount. Determine how much each side should be extended,
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x=amount each side is increased; L=length=30m; W=width=14m
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(L+x)(W+x)=2LW
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(30m+x)(14m+x)=2(30m)(14m)
420+44x+x^2=840
x^2+44x-420=0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B44x%2B-420+=+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=%2844%29%5E2-4%2A1%2A-420=3616.

Discriminant d=3616 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-44%2B-sqrt%28+3616+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2844%29%2Bsqrt%28+3616+%29%29%2F2%5C1+=+8.06659275674582
x%5B2%5D+=+%28-%2844%29-sqrt%28+3616+%29%29%2F2%5C1+=+-52.0665927567458

Quadratic expression 1x%5E2%2B44x%2B-420 can be factored:
1x%5E2%2B44x%2B-420+=+1%28x-8.06659275674582%29%2A%28x--52.0665927567458%29
Again, the answer is: 8.06659275674582, -52.0665927567458. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B44%2Ax%2B-420+%29

x=8.067m
ANSWER: Each side should be increased by 8.067 meters.
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CHECK:
(L+x)(W+x)=2LW
(30m+x)(14m+x)=2(30m)(14m)
(30m+8.067m)(14m+8.067m)=840m^2
(38.067m)(22.067m)=840m^2
840.02m^2=840m^2