How do you prove that the hypotenuse of the longest side in every right triangle $a^{2} + b^{2} > a^{2}$ $a^2+b^2>a^2$ ?

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Answer 1 · 2018-02-02T19:41:54

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$

$a^{2} = c^{2} - b^{2}$ $a^2=c^2-b^2$

$a^{2} < c^{2} \forall b > 0$ $a^2 < c^2 AA b>0$

How do you prove that the hypotenuse of the longest side in every right triangle a2+b2>a2a^2+b^2>a^2?