Plz asap *will mark brainliest * plzzz show all work

The triangle in the picture is a 45 - 45 - 90 triangle. Our pattern for the sides:

each leg: 1 unit

hypotenuse: √2 units.

So we multiply each leg by √2 to get the hypotenuse. In reverse, we divide the hypotenuse by √2 to get each leg.

We are told the hypotenuse is 6. We divide it by √2 to get each leg. Each leg is the same, so x = y.

x = 6 / √2

= 6√2 / √2 * √2 (rationalize radicals)

= 6 √2 / 2

= 3√2

Thus, x = y = 3√2