In a `DeltaPQR, PD` is the median and G is centroid. If `PG = 24 cm`, then what is the length (in cm) of PD?

Options

A. 48
B. 36
C. 60
D. 72

Answer

To solve the problem, we need to find the length of the median PD in triangle PQR, given that PG (the distance from vertex P to the centroid G) is 24 cm.

### Step-by-Step Solution:

1. **Understanding the Relationship Between PG, GD, and PD**:
- In any triangle, the centroid (G) divides the median (PD) in the ratio of 2:1. This means that PG (the distance from the vertex to the centroid) is twice the length of GD (the distance from the centroid to the midpoint of the opposite side).
- Therefore, we can express this relationship as:
\[ PG = 2 \times GD \]

2. **Finding GD**:
- We know from the problem that PG = 24 cm. Using the relationship from step 1, we can find GD:
\[ GD = \frac{PG}{2} = \frac{24 \text{ cm}}{2} = 12 \text{ cm} \]

3. **Calculating PD**:
- The total length of the median PD can be calculated by adding PG and GD together:
\[ PD = PG + GD \]
- Substituting the values we have:
\[ PD = 24 \text{ cm} + 12 \text{ cm} = 36 \text{ cm} \]

4. **Conclusion**:
- Therefore, the length of the median PD is 36 cm.

### Final Answer:
The length of PD is **36 cm**.