Final answer:
To solve for (x + y + z), we calculate the positive square roots of the given squares to find x = 30, y = 20, and z = 10. Adding them yields (x + y + z) = 60, which is not an option in the given answers. There might be a typo in the question as the calculations done with the provided squares do not match the answer choices.
Step-by-step explanation:
To find the value of (x + y + z) given x² = 900, y² = 400, and z² = 100, we first need to determine the values of x, y, and z. As x, y, and z are positive integers, we take the positive square roots:
- x = √900 = 30
- y = √400 = 20
- z = √100 = 10
Now, we add the values of x, y, and z to get:
(x + y + z) = (30 + 20 + 10) = 60.
However, the question may have a typo since the provided answer choices do not include 60. If the question meant to ask for the value of (x² + y² + z²) instead, then the calculation would be:
(x² + y² + z²) = (900 + 400 + 100) = 1400.
Again, this is not listed in the provided answer choices. Given these discrepancies, the correct answer to the intended question cannot be determined based on the available answer choices.