The areas of two similar triangles are in respectively 16 `cm^(2) and 9 cm^(2)`. Then the ratio of their corresponding sides is

Options

A. `3 : 4`
B. `2 : 3`
C. `3 : 2`
D. `4 : 3`

Answer

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

### Step 1: Understand the relationship between the areas and the sides of similar triangles.
The areas of two similar triangles are proportional to the square of the ratio of their corresponding sides. This can be expressed mathematically as:
\[ \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \left(\frac{\text{Side of Triangle 1}}{\text{Side of Triangle 2}}\right)^2 \]

### Step 2: Write down the areas of the triangles.
Given:
- Area of Triangle A (16 cm²)
- Area of Triangle B (9 cm²)

### Step 3: Set up the ratio of the areas.
Using the areas given:
\[ \frac{16}{9} = \left(\frac{\text{Side of Triangle A}}{\text{Side of Triangle B}}\right)^2 \]

### Step 4: Take the square root of both sides to find the ratio of the sides.
To find the ratio of the corresponding sides, we take the square root of both sides:
\[ \frac{\text{Side of Triangle A}}{\text{Side of Triangle B}} = \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \]

### Step 5: State the final ratio of the corresponding sides.
Thus, the ratio of the corresponding sides of the two triangles is:
\[ \frac{4}{3} \]

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

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