Answer
$x = \sqrt 2$
$y = 2$
Work Step by Step
In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, we know that the legs are equal to one another. Since one leg measures $\sqrt 2$, $x$ also equals $\sqrt 2$.
The hypotenuse is $\sqrt 2$ times each leg. Let's write an equation to solve for $y$, the length of the hypotenuse:
$y = \sqrt 2(\sqrt 2)$
Multiply the radicals:
$y = \sqrt 4$
Take the positive square root to solve for $y$:
$y = 2$
