SOLUTION: A rectangular garden has an area of 84 sq meters and a perimeter of 38 meters. Find its length.

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Question 982518: A rectangular garden has an area of 84 sq meters and a perimeter of 38 meters. Find its length.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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L=length; W=width; A=Area; P=perimeter
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P=2(L+W)
38m=2(L+W)
19m=L+W
19m-L=W
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A=LW
84m^2=LW
84m^2=L(19m-L)
84m^2=19Lm-L^2
0=-L^2+19Lm-84m^2
0=L^2-19Lm+84m^2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B-19L%2B84+=+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=%28-19%29%5E2-4%2A1%2A84=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+25+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+12
L%5B2%5D+=+%28-%28-19%29-sqrt%28+25+%29%29%2F2%5C1+=+7

Quadratic expression 1L%5E2%2B-19L%2B84 can be factored:
1L%5E2%2B-19L%2B84+=+1%28L-12%29%2A%28L-7%29
Again, the answer is: 12, 7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-19%2Ax%2B84+%29

Length is 12 meters or 7 meters
(If length is 12m, width is 7m, if length is 7m width is 12m)