SOLUTION: Can a rectangle with a perimeter of 36 meters have an area of 120 sq. meters?? And how to show your work?

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Question 874855: Can a rectangle with a perimeter of 36 meters have an area of 120 sq. meters?? And how to show your work?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A = Lw
(w-18)w = 120m^2
w^2 - 18w - 120 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-18x%2B-120+=+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=%28-18%29%5E2-4%2A1%2A-120=804.

Discriminant d=804 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+804+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+804+%29%29%2F2%5C1+=+23.1774468787578
x%5B2%5D+=+%28-%28-18%29-sqrt%28+804+%29%29%2F2%5C1+=+-5.17744687875783

Quadratic expression 1x%5E2%2B-18x%2B-120 can be factored:
1x%5E2%2B-18x%2B-120+=+1%28x-23.1774468787578%29%2A%28x--5.17744687875783%29
Again, the answer is: 23.1774468787578, -5.17744687875783. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B-120+%29