Answer
$G$
Work Step by Step
We have a special right triangle in which the two remaining angles are $45^{\circ}$. In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, the hypotenuse is $\sqrt 2$ times each leg. Let's write an equation to solve for $y$, the length of the hypotenuse:
$y = \sqrt 2(8)$
Let's rewrite $y$ in a more conventional form:
$y = 8\sqrt 2$
The answer is option $G$.
