The areas of two similar triangles are 121 `cm^(2)` and `64 cm^(2)` respectively. If the median of the first triangle is 12.1 cm, then the corresponding median of the other is :

Options

A. 6.4 cm
B. 10 cm
C. 8.8 cm
D. 3.2 cm

Answer

To find the corresponding median of the second triangle given the areas of two similar triangles, we can follow these steps:

### Step 1: Identify the areas of the triangles
The areas of the two similar triangles are given as:
- Area of Triangle 1 = 121 cm²
- Area of Triangle 2 = 64 cm²

### Step 2: Calculate the ratio of the areas
To find the ratio of the areas, we can write it as:
\[ \text{Ratio of areas} = \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \frac{121}{64} \]

### Step 3: Find the ratio of the medians
Since the triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding medians. Let the median of Triangle 1 be \( m_1 = 12.1 \) cm and the median of Triangle 2 be \( m_2 \). Thus, we have:
\[ \frac{121}{64} = \left(\frac{m_1}{m_2}\right)^2 \]

### Step 4: Take the square root of the ratio of the areas
Taking the square root of both sides gives us the ratio of the medians:
\[ \frac{m_1}{m_2} = \sqrt{\frac{121}{64}} = \frac{11}{8} \]

### Step 5: Set up the equation
We can now set up the equation using the known median:
\[ \frac{12.1}{m_2} = \frac{11}{8} \]

### Step 6: Cross-multiply to solve for \( m_2 \)
Cross-multiplying gives us:
\[ 12.1 \cdot 8 = 11 \cdot m_2 \]
\[ 96.8 = 11 \cdot m_2 \]

### Step 7: Solve for \( m_2 \)
Now, divide both sides by 11:
\[ m_2 = \frac{96.8}{11} = 8.8 \text{ cm} \]

### Final Answer:
The corresponding median of the second triangle is \( 8.8 \) cm.

---