1. The problem involves right triangles with a 45° angle and finding relationships between sides. 2. In a right triangle with a 45° angle, the sides opposite and adjacent to the angle are equal, and the hypotenuse is $\sqrt{2}$ times the length of either leg. 3. The formula relating the legs $x$ and $y$ and the hypotenuse $h$ is: $$h = x\sqrt{2} = y\sqrt{2}$$ 4. For example, if $y=4$, then the hypotenuse is: $$h = 4\sqrt{2}$$ 5. If the hypotenuse is given, say $h = \frac{9\sqrt{2}}{2}$, then each leg is: $$x = y = \frac{h}{\sqrt{2}} = \frac{\frac{9\sqrt{2}}{2}}{\sqrt{2}} = \frac{9\cancel{\sqrt{2}}}{2\cancel{\sqrt{2}}} = \frac{9}{2}$$ 6. This shows how to find missing sides using the properties of 45° right triangles. Final answer example: If $y=4$, then $x=4$ and $h=4\sqrt{2}$.