Question 1196673
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We know {{{ c = sqrt(a^2 + b^2) }}} because of the given information.
Scale (a,b,c) by R:  this results in a triangle with sides (Ra, Rb, Rc).

Now notice  
{{{ sqrt((Ra)^2 + (Rb)^2) }}} 
= {{{sqrt(R^2a^2 + R^2b^2) }}}
= {{{ sqrt(R^2(a^2+b^2)) }}}
= {{{R*sqrt(a^2 + b^2) }}} 
= Rc

The interpretation: scaling a triangle that has sides corresponding to a Pythagorean triple preserves the Pythagorean relationship between the legs and the hypotenuse.