SOLUTION: the width of a rectangular parking lot is 57 ft less than its length. determine the dimensions of the parking lot if it measures 250 ft diagonally.

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Question 860158: the width of a rectangular parking lot is 57 ft less than its length. determine the dimensions of the parking lot if it measures 250 ft diagonally.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-114x%2B-59251+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-114%29%5E2-4%2A2%2A-59251=487004.

  

  Discriminant d=487004 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--114%2B-sqrt%28+487004+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-114%29%2Bsqrt%28+487004+%29%29%2F2%5C2+=+202.964179704603

    x%5B2%5D+=+%28-%28-114%29-sqrt%28+487004+%29%29%2F2%5C2+=+-145.964179704603

    

    Quadratic expression 2x%5E2%2B-114x%2B-59251 can be factored:

  2x%5E2%2B-114x%2B-59251+=+2%28x-202.964179704603%29%2A%28x--145.964179704603%29

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

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-114%2Ax%2B-59251+%29