Why is the diagonal of any rectangular prism always longer than one side?

Answer 1

will prove by contradiction, for legs x and y .

suppose the diagonal is LESS than side x

sqrt(x^2+y^2) < x

x^2 + y^2 < x^2 <-- squares both sides

y^2 < 0

this is a contradiction: the square of a positive number must be zero or more.