Answer
$c^{2}=a^{2}+b^{2}$
Work Step by Step
$y$ varies directly with $x,$ or $y$ is directly proportional to $x$,
if there is a nonzero number $k$ such that$\ \ y=kx.$
The number $k$ is called the constant of proportionality.
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Here, y is "the square of c", and
x = "the sum of squares of a and b"
The given model is
$ c^{2}=k(a^{2}+b^{2})\quad$
Given that $k=1,$ it means that
$c^{2}=a^{2}+b^{2}$
