SOLUTION: A rectangular dog pen must have an area of 300 square feet. The length must be 50 feet longer than the width. What are the dimensions of the pen. The width is ? The length i

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Question 863803: A rectangular dog pen must have an area of 300 square feet. The length must be 50 feet longer than the width. What are the dimensions of the pen.
The width is ?
The length is?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,



A = Lw =(w+50)w =  300ft^2

         w^2 + 50x - 300 = 0

       


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B50x%2B-300+=+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=%2850%29%5E2-4%2A1%2A-300=3700.

  

  Discriminant d=3700 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-50%2B-sqrt%28+3700+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%2850%29%2Bsqrt%28+3700+%29%29%2F2%5C1+=+5.4138126514911

    x%5B2%5D+=+%28-%2850%29-sqrt%28+3700+%29%29%2F2%5C1+=+-55.4138126514911

    

    Quadratic expression 1x%5E2%2B50x%2B-300 can be factored:

  1x%5E2%2B50x%2B-300+=+1%28x-5.4138126514911%29%2A%28x--55.4138126514911%29

  Again, the answer is: 5.4138126514911, -55.4138126514911.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B50%2Ax%2B-300+%29