SOLUTION: a rectangle has an area of 36 inches squared cm2 and a perimeter of 54 cm . find the dimensions

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Question 932124: a rectangle has an area of 36 inches squared cm2 and a perimeter of 54 cm . find the dimensions
Found 2 solutions by Alan3354, ewatrrr:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a rectangle has an area of 36 inches squared cm2 and a perimeter of 54 cm 2. find the dimensions
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Is it inches or cm?
The perimeter is not sq cm, just cm.
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Assuming the units match:
L*W = 36
2L + 2W = 54 --> L + W = 27
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L*W = 36
W*(27-W) = 36
W^2 - 27W + 36 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-27x%2B36+=+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=%28-27%29%5E2-4%2A1%2A36=585.

Discriminant d=585 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+585+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+585+%29%29%2F2%5C1+=+25.5933866224478
x%5B2%5D+=+%28-%28-27%29-sqrt%28+585+%29%29%2F2%5C1+=+1.40661337755218

Quadratic expression 1x%5E2%2B-27x%2B36 can be factored:
1x%5E2%2B-27x%2B36+=+%28x-25.5933866224478%29%2A%28x-1.40661337755218%29
Again, the answer is: 25.5933866224478, 1.40661337755218. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-27%2Ax%2B36+%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

     .

 2L + 2w =54cm

L + w = 27cm

L = (27-w)

.....

A = Lw

(27-w)w = 36cm^2

w^2 - 27w + 36 = 0

w = 25.5933866224478, 1.40661337755218

Dimensions are:

25.6 by 1.4



 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-27x%2B36+=+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=%28-27%29%5E2-4%2A1%2A36=585.

  

  Discriminant d=585 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+585+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+585+%29%29%2F2%5C1+=+25.5933866224478

    x%5B2%5D+=+%28-%28-27%29-sqrt%28+585+%29%29%2F2%5C1+=+1.40661337755218

    

    Quadratic expression 1x%5E2%2B-27x%2B36 can be factored:

  1x%5E2%2B-27x%2B36+=+1%28x-25.5933866224478%29%2A%28x-1.40661337755218%29

  Again, the answer is: 25.5933866224478, 1.40661337755218.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-27%2Ax%2B36+%29