Hi,

     .

L + w = 16 

L = 16-w

Pythagorean Theorem

(16-w)^2 + w^2 = (w+8)^2

256 - 32w + w^2 + w^2 = w^2 + 16w + 64

w^2 -48w +192 = 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 : .

  

  Discriminant d=1536 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 43.5959179422654, 4.40408205773458.
Here's your graph:



  

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