Hi,

     .

The perimeter of a rectangular garden is 22.5m...The area is 12.5m^2

L + w = 11.25

L = (11.25-w)

A = Lw

(11.25-w)w = 12.5m^2

w^2 - 22.5w + 12.5 = 0



the dimensions of the garden: 21.93m by  0.57m



 
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=456.25 is greater than zero. That means that there are two solutions: .

  

    

    

    

    Quadratic expression  can be factored:

  

  Again, the answer is: 21.9300046816469, 0.569995318353087.
Here's your graph:



  

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