The areas of two similar triangles are 121 sq.m and 64 sq. m. If the median of the `1^(st)` triangle = 12.1 m, then the median of the `2^(nd)` triangle will be

Options

A. 6.4 m
B. 8.4 m
C. 8.8 m
D. 9.2 m

Answer

To solve the problem, we will use the properties of similar triangles and the relationship between their areas and corresponding medians.

### Step-by-Step Solution:

1. **Identify the Areas of the Triangles**:
- Area of the first triangle (A1) = 121 sq.m
- Area of the second triangle (A2) = 64 sq.m

2. **Find the Ratio of the Areas**:
- The ratio of the areas of two similar triangles is given by:
\[ \frac{A1}{A2} = \frac{121}{64} \]

3. **Calculate the Ratio of the Sides**:
- Since the triangles are similar, the ratio of their corresponding sides (and medians) is the square root of the ratio of their areas:
\[ \frac{\text{Side of Triangle 1}}{\text{Side of Triangle 2}} = \sqrt{\frac{A1}{A2}} = \sqrt{\frac{121}{64}} = \frac{11}{8} \]

4. **Use the Ratio to Find the Median of the Second Triangle**:
- Given that the median of the first triangle (M1) is 12.1 m, we can find the median of the second triangle (M2) using the ratio of the medians:
\[ \frac{M1}{M2} = \frac{11}{8} \]
- Rearranging gives:
\[ M2 = M1 \times \frac{8}{11} \]
- Substituting the value of M1:
\[ M2 = 12.1 \times \frac{8}{11} \]

5. **Calculate M2**:
- Performing the multiplication:
\[ M2 = 12.1 \times \frac{8}{11} = 12.1 \times 0.7272 \approx 8.8 \text{ m} \]

### Final Answer:
The median of the second triangle is approximately **8.8 m**.