Is it always true that if the right angled triangle with is also isosceles and having lengths that can be denoted in terms of a rational number, the length of its hypotenuse will always be an irrational number? Another way to look at it would be that the diagonal of a square is always irrational. Does this always hold true?
[Math] Irrational numbers and Pythagoras Theorem
irrational-numberspythagorean triples
Best Answer
If the adjacent sides of a right triangle are sqrt(2) then the hypotenuse will be 2 which is rational. However if the side lengths are rational then a$^2$+b$^2$=c$^2$ so 2a$^2$=c$^2$ and c = $\sqrt{2a}$ which is irrational since $\sqrt{2}$ is irrational and a is rational.