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,

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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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3616 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8.06659275674582, -52.0665927567458. Here's your graph:

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
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