SOLUTION: The perimeter of a rectangle is 32m. The length of the diagonal is 8 m more than its width. Find the dimensions of the rectangle.

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Question 913316: The perimeter of a rectangle is 32m. The length of the diagonal is 8 m more than its width. Find the dimensions of the rectangle.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-48x%2B192+=+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=%28-48%29%5E2-4%2A1%2A192=1536.

  

  Discriminant d=1536 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--48%2B-sqrt%28+1536+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+1536+%29%29%2F2%5C1+=+43.5959179422654

    x%5B2%5D+=+%28-%28-48%29-sqrt%28+1536+%29%29%2F2%5C1+=+4.40408205773458

    

    Quadratic expression 1x%5E2%2B-48x%2B192 can be factored:

  1x%5E2%2B-48x%2B192+=+1%28x-43.5959179422654%29%2A%28x-4.40408205773458%29

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

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-48%2Ax%2B192+%29