Answer:
In an isosceles right triangle, the length of the hypotenuse is √2 times the length of each leg. So the length of each leg is
(16√10)/√2 = 16√5
This is also the length of the hypotenuse of the 30°-60°-90° triangle. In this triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
So x = (16/2)√5 = 8√5 and y = 8√5√3 = 8√15.