Areas of two similar triangles are i the ratio of 5:3, then the ratio of their corresponding sides is :

Options

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

Answer

To solve the problem, we need to find the ratio of the corresponding sides of two similar triangles given that their areas are in the ratio of 5:3.

### 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. This can be expressed as:
\[ \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \left(\frac{\text{Side 1}}{\text{Side 2}}\right)^2 \]

2. **Set up the ratio of the areas:**
- According to the problem, the areas of the two triangles are in the ratio of 5:3. Therefore, we can write:
\[ \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \frac{5}{3} \]

3. **Relate the area ratio to the side ratio:**
- Using the relationship from step 1, we can set up the equation:
\[ \frac{5}{3} = \left(\frac{\text{Side 1}}{\text{Side 2}}\right)^2 \]

4. **Take the square root of both sides to find the ratio of the sides:**
- To find the ratio of the sides, we take the square root of both sides:
\[ \frac{\text{Side 1}}{\text{Side 2}} = \sqrt{\frac{5}{3}} \]

5. **Simplify the square root:**
- We can express this as:
\[ \frac{\text{Side 1}}{\text{Side 2}} = \frac{\sqrt{5}}{\sqrt{3}} \]

6. **Final answer:**
- Thus, the ratio of the corresponding sides of the two triangles is:
\[ \text{Side 1 : Side 2} = \sqrt{5} : \sqrt{3} \]