Answer:
(c) 6√2
Step-by-step explanation:
As with many multiple-choice problems, eliminating the impossible answers will give you the correct one.
Limits on z
The length marked z is the hypotenuse of the middle-sized triangle, so is longer than the legs of that triangle:
8 < z
The length marked z is also the long side of the largest triangle, so will be shorter than the hypotenuse of that triangle:
z < (1+8)
These limits tell you ...
8 < z < 9
The only answer choice in that range is 6√2 ≈ 8.5.
z = 6√2
Detailed working
All of the right triangles are similar, so the ratios of long leg to hypotenuse are the same for all:
8/z = z/(1+8)
72 = z² . . . . . . . . . . . cross multiply
z = √72 = 6√2 . . . . . take the square root and simplify
