Hi,

Let x represent length.  Then width is (x-57)

 x^2 + (x-57)^2 = 62500

 2x^2 - 114x + 3249 = 62500  

  2x^2 - 114x -59251 = 0

  ~203ft by 146

 


 
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=487004 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 202.964179704603, -145.964179704603.
Here's your graph:



 

 

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