Final answer:
Given the contradictory conditions that x is greater than y but their square roots are equal, there seems to be an error in the problem statement. Without additional information or context, especially concerning the term 'adjacent line for z', it is not possible to provide a definitive solution to the provided options.
Step-by-step explanation:
To solve the problem, we first need to consider the given conditions. We know that x is greater than y and that the square root of y is equal to the square root of x. However, if x > y, their square roots cannot be equal unless both x and y are equal, which contradicts x > y.
Therefore, we are likely dealing with an error in the given conditions. Assuming this error is an oversight, and interpreting the question to find the relationship between z to x and y when x and y are equal (since their square roots are equal), we would imply that z is equal to either x or y when x equals y, depending on the actual relationship intended to be described which is not given clearly.
However, without a clear definition of 'adjacent line' in the context of z in the question, we cannot provide a definitive answer to the options (A) z = x, (B) z = y, (C) z = √x, (D) z = √y. Normally, in a geometrical context, the adjective 'adjacent' would relate to the sides of a geometric figure, such as a triangle where Pythagorean theorem might be applied. But without further context, it's impossible to relate z to x or y in a meaningful way.