>>Which natural numbers occur as the area of a right triangle with three rational sides?
>>5 is the smallest number that can be used.
>
>Assuming you mean that all 3 sides must have an integer length, and the area must be an integer area, there are at least 2 such triangles:
>
>3-4-5, area 6
>5-12-13, area 30

I can't make any sense out of the question myself. Rational numbers are the set of all real numbers that can be written as a ratio of integers with a nonzero denominator. So the question seems to say that all three sides must be expressed as ratios (ie - rational). It is beyond my ken.