Area of two similar triangles are in the ratio of 5:3 then the ratio of their corresponding sides is :

Options

A. `5:3`
B. `25:9`
C. `9:25`
D. `sqrt(5) : sqrt(3)`

Answer

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

### Step-by-Step Solution:

1. **Understand the relationship between the areas and sides of similar triangles**:
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. If the areas of the triangles are in the ratio \( \frac{A_1}{A_2} \), 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.

2. **Set up the ratio of the areas**:
According to the problem, the areas of the two triangles are in the ratio \( 5:3 \). Therefore, we can write:
\[ \frac{A_1}{A_2} = \frac{5}{3} \]

3. **Relate the area ratio to the side ratio**:
Using the relationship from step 1, we can substitute the area ratio:
\[ \frac{5}{3} = \left(\frac{s_1}{s_2}\right)^2 \]

4. **Take the square root of both sides**:
To find the ratio of the sides, we take the square root of both sides:
\[ \frac{s_1}{s_2} = \sqrt{\frac{5}{3}} \]

5. **Simplify the ratio**:
We can express the ratio in a simpler form:
\[ \frac{s_1}{s_2} = \frac{\sqrt{5}}{\sqrt{3}} \]

### Final Answer:
The ratio of the corresponding sides of the two similar triangles is:
\[ \frac{s_1}{s_2} = \frac{\sqrt{5}}{\sqrt{3}} \]