SOLUTION: what are the dimensions of the rectangle with this perimeter and an area of 5 square meter?

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Question 273813: what are the dimensions of the rectangle with this perimeter and an area of 5 square meter?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
a=lw
p=2l+2w
if a=p and p=5
then 5=lw l=5/w
5=2%285%2Fw%29%2B2w
5=%2810%2Fw%29%2B2w%28w%2Fw%29
5=10%2Fw%2B2w%5E2%2Fw
5w=%28%282w%5E2%2B10%29%2Fw%29w
5w=2w%5E2%2B10
0=2w%5E2-5w%2B10
according to the solver there are no real numbers that "w" could be and that would be the same for "l" so this problem isnt possible unless u use imagenary numbers
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 2w%5E2%2B-5w%2B10+=+0) has the following solutons:

w%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=%28-5%29%5E2-4%2A2%2A10=-55.

The discriminant -55 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 -55 is + or - sqrt%28+55%29+=+7.41619848709566.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B10+%29