In the above diagram, what is the length of side XZ?

Here are the solutions for questions 8 and 9:

8. In the above diagram, what is the length of side XZ?

Step 1: Identify the given information and the unknown.
We have a right-angled triangle $\triangle XYZ$ with the right angle at $Y$.
The lengths of the two legs are $XY = 8 \text{ cm}$ and $YZ = 12 \text{ cm}$.
We need to find the length of the hypotenuse $XZ$.

Step 2: Apply the Pythagorean theorem.
The Pythagorean theorem states $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse.

$$XZ^2 = XY^2 + YZ^2$$

Step 3: Substitute the given values and calculate.

$$XZ^2 = (8 \text{ cm})^2 + (12 \text{ cm})^2$$ $$XZ^2 = 64 \text{ cm}^2 + 144 \text{ cm}^2$$ $$XZ^2 = 208 \text{ cm}^2$$ $$XZ = \sqrt{208 \text{ cm}^2}$$ $$XZ \approx 14.422 \text{ cm}$$

Step 4: Select the closest option.
Comparing this value to the given options: