The length of a rectangular room is 4 metres. If it can be partitioned into two equal square rooms. What is the length of each partition in metre ?

Options

A. A)1
B. B)2
C. C)4
D. D)Data inadequate

Answer

To solve the problem step by step, we need to find the length of each partition when a rectangular room of length 4 meters is divided into two equal square rooms.

### Step 1: Understand the problem
We have a rectangular room with a length of 4 meters. We need to partition this room into two equal square rooms.

### Step 2: Set up the variables
Let the width of the rectangular room be denoted as \( B \). The area of the rectangular room can be calculated using the formula:
\[ \text{Area of rectangle} = \text{Length} \times \text{Width} = 4 \times B \]

### Step 3: Determine the area of the square rooms
Since the rectangular room is being partitioned into two equal square rooms, let the side length of each square room be \( A \). The area of one square room is:
\[ \text{Area of one square} = A^2 \]
Thus, the total area of the two square rooms is:
\[ \text{Total area of squares} = 2 \times A^2 \]

### Step 4: Set the areas equal
Since the total area of the rectangular room must equal the total area of the two square rooms, we can set up the equation:
\[ 4B = 2A^2 \]

### Step 5: Simplify the equation
We can simplify the equation by dividing both sides by 2:
\[ 2B = A^2 \]

### Step 6: Solve for \( A \)
To find \( A \), we can rearrange the equation:
\[ A^2 = 2B \]
Taking the square root of both sides gives us:
\[ A = \sqrt{2B} \]

### Step 7: Conclusion
The length of each partition (the side of each square room) is given by \( A = \sqrt{2B} \). However, since the width \( B \) is not provided in the question, we cannot determine a specific numerical value for \( A \). Therefore, the answer is that the data is insufficient to determine the exact length of each partition.