Triangle PQR is such that PQ= 9cm, QR= 6cm, PR 7.5cm and triangle PQR is similar to triangle XYZ. If XY= 18cm, find the value of YZ.
A. 15cm B. 18cm C. 12cm D. 9cm

Options

A. A
B. C
C. B
D. D

Answer

To solve the problem, we need to use the property of similar triangles, which states that the ratios of the corresponding sides of similar triangles are equal.

### Step-by-Step Solution:

1. **Identify the sides of triangle PQR and triangle XYZ:**
- For triangle PQR:
- PQ = 9 cm
- QR = 6 cm
- PR = 7.5 cm
- For triangle XYZ:
- XY = 18 cm
- YZ = ? (this is what we need to find)
- ZX = ? (not needed for this question)

2. **Set up the ratio of the corresponding sides:**
Since triangle PQR is similar to triangle XYZ, we can set up the following ratio:
\[ \frac{PQ}{XY} = \frac{QR}{YZ} \]

3. **Substitute the known values into the ratio:**
We know that:
- PQ = 9 cm
- XY = 18 cm
- QR = 6 cm
- YZ = ?

Substitute these values into the ratio:
\[ \frac{9}{18} = \frac{6}{YZ} \]

4. **Simplify the left side of the equation:**
\[ \frac{9}{18} = \frac{1}{2} \]
So, we can rewrite the equation as:
\[ \frac{1}{2} = \frac{6}{YZ} \]

5. **Cross-multiply to solve for YZ:**
Cross-multiplying gives:
\[ 1 \cdot YZ = 2 \cdot 6 \]
\[ YZ = 12 \]

6. **Conclusion:**
The value of YZ is 12 cm.

### Final Answer:
C. 12 cm