SOLUTION: The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 106cm^2 , what is the length of the diagonal?

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Question 51223: The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 106cm^2 , what is the length of the diagonal?
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
length = l
width = 2l - 2
l(2l - 2) = 106
2l^2 - 2l - 106 = 0
l^2 - l - 53 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -211 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -211 is + or - .

The solution is

Here's your graph:

No rectangle exists.
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