(b) < √2c
Since a, b, c are the lengths of the sides of a right triangle having hypotenuse of length c, therefore a2 + b2 = c2
(Pythagoras, Theoram)
Now, a > 0, b > 0 ⇒ (a – b)2 > 0
⇒ a2 + b2 > 2ab
⇒ 2(a2 + b2) > a2 + b2 + 2ab
⇒ 2 (a2 + b2) > (a + b)2
⇒ 2c2 > (a + b)2 ⇒ (a + b)2 < 2c2 ⇒ (a + b) < √2c.