SOLUTION: the length of a rectangular plot is 8 m greater than its breadth.of the area of the plot is 308 m^,the length of the plot is

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Question 954458: the length of a rectangular plot is 8 m greater than its breadth.of the area of the plot is 308 m^,the length of the plot is

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=length=W+8m; W=breadth=L-8m; A=area=308m^2
A=L*W
308m%5E2=L%2AW Substitute for W.
308m%5E2=L%28L-8m%29
308m%5E2=L%5E2-8Lm Subtract 308m^2 from each side.
0=L%5E2-8Lm-308m%5E2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B-8L%2B-308+=+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=%28-8%29%5E2-4%2A1%2A-308=1296.

Discriminant d=1296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+1296+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+1296+%29%29%2F2%5C1+=+22
L%5B2%5D+=+%28-%28-8%29-sqrt%28+1296+%29%29%2F2%5C1+=+-14

Quadratic expression 1L%5E2%2B-8L%2B-308 can be factored:
1L%5E2%2B-8L%2B-308+=+1%28L-22%29%2A%28L--14%29
Again, the answer is: 22, -14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-308+%29

ANSWER: The length is 22 meters
CHECK:
W=L-8m=22m-8m=14m The breadth is 14 meters.
A=L%2AW
308m%5E2=22m%2A14m
308m%5E2=308m%5E2