In the following questions, each question has four options (A), (B), (C) and (D). Choose the correct option and indicate your correct response.
The perimeter of a rectangle and a square is same. Length and breadth of rectangle are 10 cm and 8 cm respectively. What is the area of square?

Options

A. 144 sq. cm
B. 36 sq. cm
C. 81 sq. cm
D. 64 sq. cm

Answer

To solve the problem, we need to find the area of a square given that the perimeter of the square is the same as the perimeter of a rectangle with specific dimensions.

### Step-by-Step Solution:

1. **Calculate the perimeter of the rectangle:**
- The formula for the perimeter of a rectangle is given by:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Breadth}) \]
- Here, the length is 10 cm and the breadth is 8 cm.
- Substitute the values into the formula:
\[ \text{Perimeter} = 2 \times (10 \, \text{cm} + 8 \, \text{cm}) = 2 \times 18 \, \text{cm} = 36 \, \text{cm} \]

2. **Set the perimeter of the square equal to the perimeter of the rectangle:**
- Since the perimeter of the square is the same as the perimeter of the rectangle, we have:
\[ \text{Perimeter of square} = 36 \, \text{cm} \]

3. **Use the perimeter of the square to find the side length:**
- The formula for the perimeter of a square is:
\[ \text{Perimeter} = 4 \times \text{Side} \]
- Let the side of the square be \( a \) cm. Therefore, we can write:
\[ 4a = 36 \, \text{cm} \]
- To find \( a \), divide both sides by 4:
\[ a = \frac{36}{4} = 9 \, \text{cm} \]

4. **Calculate the area of the square:**
- The formula for the area of a square is:
\[ \text{Area} = \text{Side}^2 \]
- Substitute the value of \( a \):
\[ \text{Area} = 9 \, \text{cm} \times 9 \, \text{cm} = 81 \, \text{cm}^2 \]

### Final Answer:
The area of the square is \( 81 \, \text{cm}^2 \).