If ratio of areas of two triangles are `64 : 121` , then the ratio of corresponding perimeter is

Options

A. ` 8 : 11`
B. `11 : 8`
C. `9 : 121`
D. `8 : 9`

Answer

To solve the problem, we need to find the ratio of the corresponding perimeters of two triangles given the ratio of their areas.

### Step-by-Step Solution:

1. **Understanding the Given Ratio of Areas**:
We are given that the ratio of the areas of two triangles is \( 64 : 121 \).

2. **Using the Property of Similar Triangles**:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, if the ratio of areas is \( \frac{A_1}{A_2} = \frac{64}{121} \), we can express this in terms of the ratio of the sides (let's denote it as \( k \)):
\[ \frac{A_1}{A_2} = k^2 \]

3. **Finding the Ratio of Sides**:
To find \( k \), we take the square root of the ratio of the areas:
\[ k = \sqrt{\frac{64}{121}} = \frac{\sqrt{64}}{\sqrt{121}} = \frac{8}{11} \]
So, the ratio of the corresponding sides of the triangles is \( 8 : 11 \).

4. **Finding the Ratio of Perimeters**:
The perimeter of a triangle is the sum of the lengths of its sides. For similar triangles, the ratio of their perimeters is the same as the ratio of their corresponding sides. Therefore, the ratio of the perimeters \( P_1 \) and \( P_2 \) of the two triangles is:
\[ \frac{P_1}{P_2} = k = \frac{8}{11} \]

5. **Conclusion**:
Hence, the ratio of the corresponding perimeters of the two triangles is \( 8 : 11 \).

### Final Answer:
The ratio of the corresponding perimeters of the two triangles is \( 8 : 11 \).

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