In `DeltaPQR`, ray PS is the bisector of `/_QPR`.
`Q-S-R`. If `QS=4.8 cm, SR=3.6cm` then find `PQ:PR`.

Explanation

To solve the problem, we will use the Angle Bisector Theorem, which states that the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the lengths of the other two sides of the triangle.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- In triangle \( PQR \), ray \( PS \) is the bisector of angle \( QPR \).
- Lengths given: \( QS = 4.8 \, \text{cm} \) and \( SR = 3.6 \, \text{cm} \).

2. **Apply the Angle Bisector Theorem:**
- According to the Angle Bisector Theorem:
\[ \frac{QS}{SR} = \frac{PQ}{PR} \]
- Substituting the given values:
\[ \frac{4.8}{3.6} = \frac{PQ}{PR} \]

3. **Simplify the Ratio:**
- To simplify \( \frac{4.8}{3.6} \), we can eliminate the decimals by multiplying both the numerator and the denominator by 10:
\[ \frac{48}{36} \]
- Now, simplify \( \frac{48}{36} \) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 12:
\[ \frac{48 \div 12}{36 \div 12} = \frac{4}{3} \]

4. **Express the Ratio:**
- Therefore, we have:
\[ \frac{PQ}{PR} = \frac{4}{3} \]
- This can be expressed as:
\[ PQ : PR = 4 : 3 \]

5. **Final Answer:**
- The required ratio \( PQ : PR \) is \( 4 : 3 \).