If the ratio of areas of two similar triangles is 9:16 then the ratio of their corresponding sides is

Options

A. 3:5
B. 3:4
C. 4:5
D. 4:3

Answer

To find the ratio of the corresponding 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 ratio of the areas of two similar triangles is 9:16.

2. **Use the Property of Similar Triangles**:
For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. This can be expressed as:
\[ \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \left(\frac{\text{Side of Triangle 1}}{\text{Side of Triangle 2}}\right)^2 \]

3. **Set Up the Equation**:
Let the ratio of the corresponding sides be \( \frac{a}{b} \). Then we can write:
\[ \frac{9}{16} = \left(\frac{a}{b}\right)^2 \]

4. **Take the Square Root**:
To find the ratio of the corresponding sides, we take the square root of both sides:
\[ \frac{a}{b} = \sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4} \]

5. **Conclusion**:
Therefore, the ratio of the corresponding sides of the two triangles is \( 3:4 \).

### Final Answer:
The ratio of their corresponding sides is \( 3:4 \).

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