SOLUTION: I'm a retired math and physics teacher. I'm refering to the problem in the examples page with a rectangle of 90 cm^2 and consecutive integer sides of x and x+1. Are you folk

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Question 129019: I'm a retired math and physics teacher.
I'm refering to the problem in the examples page with a rectangle
of 90 cm^2 and consecutive integer sides of x and x+1.
Are you folks aware that there are many, many solutions
to this problem? :)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I was not aware that there were many solutions to such a problem and I would be very interested in learning about these.
I did not do the example to which you refer but, had I done so, I would have done the following:
For a rectangle:
A+=+L%2AW You say that the area, A = 90 sq.cm
The sides are consecutive integers x and x+1, so:
90+=+x%28x%2B1%29
90+=+x%5E2%2Bx or...
x%5E2%2Bx-90+=+0 Factoring the quadratic, we get:
%28x-9%29%28x%2B10%29+=+0 so that...
x+=+9 or x+=+-10 We'll take the positive value as lengths are positive:
x+=+9 and x%2B1+=+10 and...
9%2A10+=+90