Hi,

Let x represent the length.  The width is (x+5)

x(x+5) = 124cm^2

x^2  + 5x = 124

x^2 + 5x - 124 = 0

 x = `8.9, the length.  The width ` 13.9

 


 
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 : .

  

  Discriminant d=521 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 8.91271221051333, -13.9127122105133.
Here's your graph:



  

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