SOLUTION: The perimeter of a rectangular garden is 22.5m...The area is 12.5m2 Find the dimensions of the garden.

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Question 923822: The perimeter of a rectangular garden is 22.5m...The area is 12.5m2 Find the dimensions of the garden.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

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

w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

the dimensions of the garden: 21.93m by  0.57m




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-22.5x%2B12.5+=+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=%28-22.5%29%5E2-4%2A1%2A12.5=456.25.

  

  Discriminant d=456.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--22.5%2B-sqrt%28+456.25+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-22.5%29%2Bsqrt%28+456.25+%29%29%2F2%5C1+=+21.9300046816469

    x%5B2%5D+=+%28-%28-22.5%29-sqrt%28+456.25+%29%29%2F2%5C1+=+0.569995318353087

    

    Quadratic expression 1x%5E2%2B-22.5x%2B12.5 can be factored:

  1x%5E2%2B-22.5x%2B12.5+=+1%28x-21.9300046816469%29%2A%28x-0.569995318353087%29

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

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-22.5%2Ax%2B12.5+%29