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(6103) (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:
You say that the area, A = 90 sq.cm
The sides are consecutive integers x and x+1, so:

or...
Factoring the quadratic, we get:
so that...
or We'll take the positive value as lengths are positive:
and and...