In `DeltaXYZ`, if G is the centroid and XL is the median with length 18cm. Then the length of XG is :

Options

A. 12cm
B. 10cm
C. 14cm
D. 16cm

Answer

To find the length of XG in triangle XYZ where G is the centroid and XL is the median with a length of 18 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Median and Centroid**:
- In triangle XYZ, XL is a median, which means it connects vertex X to the midpoint L of side YZ. The centroid G divides the median into two segments: XG and GL.

2. **Ratio of the Segments**:
- The centroid divides the median in the ratio of 2:1. This means that if we denote the length of XG as 2k and GL as k, then the total length of the median XL can be expressed as:
\[ XL = XG + GL = 2k + k = 3k \]

3. **Setting Up the Equation**:
- We know from the problem that the length of the median XL is 18 cm. Therefore, we can set up the equation:
\[ 3k = 18 \]

4. **Solving for k**:
- To find k, we divide both sides of the equation by 3:
\[ k = \frac{18}{3} = 6 \]

5. **Finding XG**:
- Now that we have k, we can find the length of XG:
\[ XG = 2k = 2 \times 6 = 12 \text{ cm} \]

### Final Answer:
The length of XG is **12 cm**.

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