What is of the area of rectangle and cost of its flooring? Statements: I. The length of the rectangle is 6 meters. II. The breadth of the rectangle is two-thirds of its length. III. The cost of flooring the area of 100 `cm ^(2)` is Rs.45.

Options

A. Onlt I and III
B. Only II and III
C. Only II and III
D. Quesin cannot be answred even with data in all three statements.

Explanation

To solve the problem of finding the area of the rectangle and the cost of its flooring, we will analyze the statements provided step by step.

### Step 1: Determine the Length of the Rectangle
From Statement I, we know:
- The length of the rectangle is 6 meters.

### Step 2: Calculate the Breadth of the Rectangle
From Statement II, we know:
- The breadth of the rectangle is two-thirds of its length.
- Therefore, the breadth can be calculated as:
\[ \text{Breadth} = \frac{2}{3} \times \text{Length} = \frac{2}{3} \times 6 \text{ meters} = 4 \text{ meters} \]

### Step 3: Calculate the Area of the Rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the values we have:
\[ A = 6 \text{ meters} \times 4 \text{ meters} = 24 \text{ square meters} \]

### Step 4: Convert the Area to Square Centimeters
Since the cost of flooring is given per 100 cm², we need to convert the area from square meters to square centimeters:
\[ 1 \text{ square meter} = 10,000 \text{ square centimeters} \]
Thus,
\[ 24 \text{ square meters} = 24 \times 10,000 \text{ cm}^2 = 240,000 \text{ cm}^2 \]

### Step 5: Calculate the Cost of Flooring
From Statement III, we know:
- The cost of flooring 100 cm² is Rs. 45.
To find the cost of flooring 240,000 cm², we first find out how many 100 cm² units are in 240,000 cm²:
\[ \text{Number of 100 cm}^2 = \frac{240,000 \text{ cm}^2}{100 \text{ cm}^2} = 2400 \]
Now, we can calculate the total cost:
\[ \text{Total Cost} = 2400 \times 45 \text{ Rs.} = 108,000 \text{ Rs.} \]

### Conclusion
Thus, the area of the rectangle is 24 square meters, and the cost of flooring is Rs. 108,000.