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Relating Sides of a Triangle

What is the length ‘ $y$ ‘ expressed in terms of ‘ $x$ ‘?

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$\begin{equation*} a^2 + b^2 = c^2 \end{equation*}$

$\begin{equation*} x^2 + x^2 = \left( \frac{y}{3} \right)^2 \end{equation*}$

$\begin{equation*} \sqrt{2 x^2} = \sqrt{\left( \frac{y}{3} \right)^2} \end{equation*}$

$\begin{equation*} x \sqrt{2} = \frac{y}{3} \end{equation*}$

$\begin{equation*} 3 \left( x \sqrt{2} \right) = \left( \frac{y}{3} \right) 3 \end{equation*}$

$\begin{equation*} \boxed{3 x \sqrt{2} = y} \end{equation*}$