The length of a rectangular floor is twice its breadth. If Rs 256 is required to paint the floor at the rate of Rs 2 per square metres, then what would be the length of floor ?

Options

A. 16 meters
B. 8 meters
C. 12 meters
D. 32 meters

Answer

To find the length of the rectangular floor, we can follow these steps:

### Step 1: Define Variables
Let the breadth of the rectangular floor be \( b \) meters. According to the problem, the length \( l \) is twice the breadth. Therefore, we can express the length as:
\[ l = 2b \]

### Step 2: Calculate the Area of the Floor
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Substituting the expression for length:
\[ A = l \times b = (2b) \times b = 2b^2 \]

### Step 3: Calculate the Cost of Painting
The cost to paint the floor is given as Rs 256, and the rate of painting is Rs 2 per square meter. Therefore, we can express the total cost in terms of the area:
\[ \text{Cost} = \text{Area} \times \text{Rate} \]
Substituting the values we have:
\[ 256 = A \times 2 \]
\[ 256 = 2b^2 \]

### Step 4: Solve for \( b^2 \)
Now, we can solve for \( b^2 \):
\[ 2b^2 = 256 \]
Dividing both sides by 2:
\[ b^2 = \frac{256}{2} = 128 \]

### Step 5: Find \( b \)
Now, we take the square root of both sides to find \( b \):
\[ b = \sqrt{128} \]
\[ b = \sqrt{64 \times 2} = 8\sqrt{2} \]

### Step 6: Find the Length \( l \)
Now that we have \( b \), we can find the length \( l \):
\[ l = 2b = 2(8\sqrt{2}) = 16\sqrt{2} \]

### Conclusion
Thus, the length of the floor is:
\[ l = 16\sqrt{2} \text{ meters} \]

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