`triangle`PQR and `triangle`JWN are similar. If 3PQ = JW and WN = 9 cm, then QR is equal to

Options

A. 3 cm
B. 6cm
C. 9 cm
D. 12 cm

Answer

To solve the problem, we will use the properties of similar triangles. Given that triangle PQR is similar to triangle JWN, we can set up a proportion based on the corresponding sides of the triangles.

### Step-by-Step Solution:

1. **Identify the given information**:
- The triangles PQR and JWN are similar.
- It is given that \( 3PQ = JW \).
- The length of \( WN \) is \( 9 \) cm.

2. **Set up the proportion**:
- Since the triangles are similar, the ratios of corresponding sides are equal.
- From the information provided, we can express the ratio of the sides as:
\[ \frac{PQ}{JW} = \frac{QR}{WN} \]

3. **Substitute the known values**:
- We know that \( 3PQ = JW \), which implies:
\[ \frac{PQ}{JW} = \frac{1}{3} \]
- We also know \( WN = 9 \) cm.

4. **Set up the equation**:
- Substitute the known values into the proportion:
\[ \frac{1}{3} = \frac{QR}{9} \]

5. **Cross-multiply to solve for QR**:
- Cross-multiplying gives us:
\[ 1 \cdot 9 = 3 \cdot QR \]
- This simplifies to:
\[ 9 = 3QR \]

6. **Solve for QR**:
- Divide both sides by 3:
\[ QR = \frac{9}{3} = 3 \text{ cm} \]

### Final Answer:
Thus, the length of \( QR \) is \( 3 \) cm.

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