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
