To determine the length of $XZ$, we start by using the properties of similar triangles. When two triangles are similar, their corresponding sides are proportional.

Given triangles:

• Triangle $PQR$ with sides 7, 10, and 12.
• Triangle $XYZ$ with sides $6$, $YX$, and $XZ$.

To find $XZ$, we use the proportionality of the corresponding sides:

$\frac{PR}{XZ} = \frac{PQ}{XY}$

From the triangle similarity, let's use the side ratios:

$\frac{12}{XZ} = \frac{10}{6}$

Solving for $XZ$:

$\frac{12}{XZ} = \frac{10}{6} \implies XZ = \frac{12 \times 6}{10} = 7.2.$

Therefore, the correct length of $XZ$ is:

$\boxed{7.2}$

Would you like to discuss the steps in more detail or have any other questions?

Related Questions:

1. How do you determine if two triangles are similar?
2. What is the importance of proportionality in similar triangles?
3. Can you explain how side lengths relate to angles in similar triangles?
4. How can the Pythagorean Theorem apply to similar triangles?
5. What is the difference between congruent and similar triangles?

Tip: Always match the correct corresponding sides when working with similar triangles to avoid errors in calculations.