SOLUTION: A room is 2m longer than it is wide. If its area is 30cm2, what is its perimeter?

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Question 986989: A room is 2m longer than it is wide. If its area is 30cm2, what is its perimeter?
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-2m; A=Area=0.003m^2; P=perimeter
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LW=A
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L%28L-2m%29=0.003m%5E2
L%5E2-2L=0.003
L%5E2-2L-0.003=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B-2L%2B-0.003+=+0) has the following solutons:

L%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=%28-2%29%5E2-4%2A1%2A-0.003=4.012.

Discriminant d=4.012 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+4.012+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+4.012+%29%29%2F2%5C1+=+2.00149887668434
L%5B2%5D+=+%28-%28-2%29-sqrt%28+4.012+%29%29%2F2%5C1+=+-0.00149887668434245

Quadratic expression 1L%5E2%2B-2L%2B-0.003 can be factored:
1L%5E2%2B-2L%2B-0.003+=+1%28L-2.00149887668434%29%2A%28L--0.00149887668434245%29
Again, the answer is: 2.00149887668434, -0.00149887668434245. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-0.003+%29

Length=2.0015 meter
Width=2.0015-2=0.0015 meter
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P=2(L+W)=2(2.0015m+0.0015)=2(2.003)=4.006 meters
ANSWER: The perimeter is 4.006 meters.
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CHECK:
LW=A
%282.0015m%29%280.0015m%29=0.003m%5E2
0.003m%5E2=0.003m%5E2
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I think the problem was entered incorrectly.
A 30cm^2 room would be very small.
If the difference in length and width was in centimeters,
or the area was in square meters, you would get a different
result. Process would be the same.