different theorem? how do triangle sides have negative length?

Wrong class of numbers you’re thinking of. Irrational numbers are the ones that can’t be represented in fractions.

Example: A right triangle where both legs have length 1.

a^2^ + b^2^ =c^2^
1^2^ + 1^2^ =c^2^
1+1=c^2^
2=c^2^ => c = sqrt(2)