The given question is followed by three statements labelled I, II and III. You have to study the question and all the three statements given do decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the given question.
What is the area of the given rectangle?
I. Perimeter of the rectangle is 60 cm.
II. Breadth of the rectangle is 12 cm.
III. Sum of two adjacent sides is 30 cm.

Options

A. I only
B. II only
C. III only
D. I or III only

Answer

To find the area of the rectangle, we need to analyze the given statements one by one.

### Step-by-Step Solution:

1. **Understanding the Question**: We need to find the area of a rectangle. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]

2. **Statement I**: The perimeter of the rectangle is 60 cm.
- The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(L + B) \]
- Given \( P = 60 \):
\[ 60 = 2(L + B) \implies L + B = 30 \quad \text{(Equation 1)} \]

3. **Statement II**: The breadth of the rectangle is 12 cm.
- Let \( B = 12 \) cm.
- We can substitute this value into Equation 1:
\[ L + 12 = 30 \implies L = 30 - 12 = 18 \quad \text{(Length)} \]

4. **Calculating the Area**: Now that we have both the length and breadth:
\[ A = L \times B = 18 \times 12 = 216 \text{ cm}^2 \]

5. **Statement III**: The sum of two adjacent sides is 30 cm.
- This statement is essentially the same as Statement I, which states \( L + B = 30 \) cm. Therefore, it does not provide any new information.

### Conclusion:
- **Redundant Statements**:
- Statement I and Statement III convey the same information regarding the sum of the length and breadth. Thus, either Statement I or Statement III can be considered redundant.
- Statement II is essential as it provides the breadth needed to calculate the area.

### Final Answer:
- The area of the rectangle is \( 216 \text{ cm}^2 \).
- The redundant statements are Statement I and Statement III.