SOLUTION: what shape has a perimeter of 14 inches and the area of 8sq inches

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Question 503224: what shape has a perimeter of 14 inches and the area of 8sq inches
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
For a regular polygon with n sides of length s:
Perimeter = n*s = 14
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Area+=+8+=+ns%5E2%2Acot%28180%2Fn%29
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The area of a triangle (n=3) is:
s = 14/3
Area = 3*(14/3)^2*cot(60)
Area = 37.72
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Area of a square (n=4) is:
s = 14/4
Area = 4*(14/4)^2*cot(45)
Area = 49
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The area increases with the number of sides, so it's not a regular polygon.
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Try a parallelogram
Area = b*h/2 = 8
2b + 2h = 14
b+h = 7
h = 7-b
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b*h = 16
b*(7-b) = 16
7b - b^2 - 16 = 0
b%5E2+-+7b+%2B+16+=+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-7x%2B16+=+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=%28-7%29%5E2-4%2A1%2A16=-15.

The discriminant -15 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -15 is + or - sqrt%28+15%29+=+3.87298334620742.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B16+%29

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No real solutions.
I think there's no such plane figure.
Maybe a typo.