Areas of two similar triangles are in the ratio 64:121, then the sides of these triangles are in the ratio:

Options

A. `8:11`
B. `11:8`
C. `64:121`
D. None of these

Answer

To find the ratio of the sides of two similar triangles given the ratio of their areas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given that the areas of two similar triangles are in the ratio of 64:121.

2. **Use the Property of Similar Triangles**:
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Mathematically, if the areas are in the ratio \( A_1 : A_2 \), then:
\[ \frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2 \]
where \( s_1 \) and \( s_2 \) are the lengths of the corresponding sides of the triangles.

3. **Set Up the Equation**:
Given the areas are in the ratio \( 64:121 \), we can set up the equation:
\[ \frac{64}{121} = \left(\frac{s_1}{s_2}\right)^2 \]

4. **Take the Square Root**:
To find the ratio of the sides, we take the square root of both sides:
\[ \frac{s_1}{s_2} = \sqrt{\frac{64}{121}} \]

5. **Simplify the Square Root**:
Calculate the square root:
\[ \frac{s_1}{s_2} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \]

6. **Final Ratio of Sides**:
Therefore, the ratio of the sides of the two triangles is:
\[ s_1 : s_2 = 8 : 11 \]

### Final Answer:
The sides of the triangles are in the ratio \( 8 : 11 \).