https://file.aiquickdraw.com/mathbot/file/1729537726144ftah0ihb.jpg

To solve this, we can use the Pythagorean theorem, which applies to right-angled triangles.

The theorem states that for a right triangle:
\[
Z^2 = X^2 + 8^2
\]
where \( Z \) is the hypotenuse, \( X \) is one of the legs, and 8 cm is the other leg.

This equation simplifies to:
\[
Z^2 = X^2 + 64
\]
Taking the square root of both sides to find \( Z \):
\[
Z = \sqrt{X^2 + 64}
\]

Thus, the correct answer is:
\[
\boxed{\sqrt{X^2 + 64}}
\]

Let me know if you would like further explanation or have any questions.

Here are 5 related questions:
1. How would you calculate the value of \( X \) if \( Z \) were given?
2. What is the significance of the Pythagorean theorem in right triangles?
3. How can we determine the other leg if both \( Z \) and \( X \) are given?
4. How would the formula change if the known leg were different from 8 cm?
5. How would you use this formula to calculate \( Z \) if \( X = 6 \) cm?

**Tip:** Always ensure that the longest side in a right triangle is correctly identified as the hypotenuse before applying the Pythagorean theorem.

In the triangle, which expression can be used to calculate the value of Z in terms of X?

Learn how to calculate the value of Z in terms of X using the Pythagorean theorem. The problem involves a right triangle with a leg of 8 cm, suitable for Grades 7-10.

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