In a Pythagorean triplets, is $a + b$ always greater then $c$?

Question

I have a looked around, but the answer is nowhere to be found.

Yes. $a+b = \sqrt{(a+b)^2} > \sqrt{a^2+b^2}$ = c. – njguliyev Sep 28 '13 at 19:53 — njguliyev, Sep 28 '13 at 19:53
Yes, because $(a+b)^2> a^2+b^2=c^2$ – L. F. Sep 28 '13 at 19:53 — L. F., Sep 28 '13 at 19:53
Also, one can view it in terms of the triangle inequality. – Don Larynx Sep 28 '13 at 19:54 — Don Larynx, Sep 28 '13 at 19:54

score 4 · Answer 1 · answered Sep 28 '13 at 19:56

4

Yes. The easiest way to see this is to remember that they correspond to the three sides of a right triangle. The sum of two sides has to be larger than the remaining side. There are also algebraic proofs.

answered Sep 28 '13 at 19:56

TBrendle

3,253

In a Pythagorean triplets, is $a + b$ always greater then $c$?

1 Answers1