SOLUTION: The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 122 square centimeters, what is the length of the diagonal?

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Question 946706: The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 122 square centimeters, what is the length of the diagonal?
Answer by amarjeeth123(574) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the rectangle be x.
Width of the rectangle=2x-5
Area of the rectangle=x(2x-5)
x(2x-5)=122
2x^2-5x-122=0
x^2-2.5x-61=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2.5x%2B-61+=+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=%28-2.5%29%5E2-4%2A1%2A-61=250.25.

Discriminant d=250.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2.5%2B-sqrt%28+250.25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2.5%29%2Bsqrt%28+250.25+%29%29%2F2%5C1+=+9.15964600977819
x%5B2%5D+=+%28-%28-2.5%29-sqrt%28+250.25+%29%29%2F2%5C1+=+-6.65964600977819

Quadratic expression 1x%5E2%2B-2.5x%2B-61 can be factored:
1x%5E2%2B-2.5x%2B-61+=+1%28x-9.15964600977819%29%2A%28x--6.65964600977819%29
Again, the answer is: 9.15964600977819, -6.65964600977819. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2.5%2Ax%2B-61+%29

x=9.16
2x-5=13.32
Length of the diagonal=16.16