The following questions are accompanied by two statements I and II. You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
What is perimeter of triangle?
I . Side of triangle is equal to side of square whose area is 196 cm?
II. Side of triangle is equal to length of rectangle whose area is 484 cm?

Options

A. Statement i alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions.
B. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.
D. Either statement I or statement II by itself is sufficient to answer the question.

Answer

To solve the question about the perimeter of a triangle based on the given statements, let’s analyze each statement step by step.

### Step 1: Understand the question
We need to find the perimeter of a triangle. The perimeter of a triangle is calculated by adding the lengths of all three sides.

### Step 2: Analyze Statement I
**Statement I:** The side of the triangle is equal to the side of a square whose area is 196 cm².

1. **Calculate the side of the square:**
- The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
- Setting this equal to 196 cm², we have:
\[ \text{side}^2 = 196 \]
- Taking the square root of both sides:
\[ \text{side} = \sqrt{196} = 14 \text{ cm} \]

2. **Determine the perimeter of the triangle:**
- Since the side of the triangle is equal to the side of the square, the side of the triangle is also 14 cm.
- The perimeter of a triangle with all sides equal (assuming it’s an equilateral triangle) is:
\[ \text{Perimeter} = 3 \times \text{side} = 3 \times 14 = 42 \text{ cm} \]

### Conclusion for Statement I:
Statement I alone is sufficient to determine the perimeter of the triangle, which is 42 cm.

### Step 3: Analyze Statement II
**Statement II:** The side of the triangle is equal to the length of a rectangle whose area is 484 cm².

1. **Calculate the area of the rectangle:**
- The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{breadth} \]
- We know the area is 484 cm², but we do not have enough information to determine the length or breadth individually.

2. **Implication:**
- Without knowing either the length or breadth, we cannot determine the side of the triangle. Therefore, we cannot find the perimeter.

### Conclusion for Statement II:
Statement II alone is not sufficient to determine the perimeter of the triangle.

### Final Conclusion:
- **Statement I is sufficient** to answer the question.
- **Statement II is not sufficient** to answer the question.

Thus, the correct answer is that **only Statement I is sufficient**.