Consider the diagram below. Which of the following represent the values of x,y, and z to the nearest hundredth?

see the attached figure to better understand the problem

we know that
in the triangle BCD
y²+5.66²=z²-------> y²=z²-5.66²------> equation 1

in the triangle ABC
y²+5.66²=x²-------> y²=x²-5.66²------> equation 2

equals 1 and 2

z²-5.66²=x²-5.66²--------> z²=x²---------> z=x

if z=x then
angle A=45°
angle D=45°

in the triangle ABD
cos 45=z/(5.66*2)-------> z=11.32*cos 45-----> 11.32*√2/2----> 8
z=8
x=8

y²=z²-5.66²------> 8²-5.66²-----> y²=31.96------> y=5.65

the answer is
the value of x is 8
the value of z is 8
the value of y=5.65