when the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, the altitude equals the product of the two segments of the hypotenuse.
(w+9)²=8*18=144
w+9=12 or w+9=-12
w=3 (discard the negative number)
use the same method, z=√(9*11)=3√11
next, you can use the Pythagorean theorem to find x and y.
x=√(9²+99)=√180=6√5
y=√(11²+99)=√220=2√55