The length of a rectangular plot of land is twice its breadth. A square swimming pool of side 8 m, occupies one-eighth part of the plot. The length of the plot is:

Options

A. 64 m
B. 32 m
C. 16 m
D. 12 m

Answer

To solve the problem step by step, let's break it down:

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

### Step 2: Calculate the area of the swimming pool
The swimming pool is square with a side of 8 meters. The area \( A \) of the swimming pool can be calculated using the formula for the area of a square:
\[ A = \text{side} \times \text{side} = 8 \times 8 = 64 \text{ m}^2 \]

### Step 3: Relate the area of the swimming pool to the area of the plot
According to the problem, the swimming pool occupies one-eighth of the area of the rectangular plot. Let \( A_p \) be the area of the plot. Thus, we have:
\[ \frac{1}{8} A_p = 64 \]

### Step 4: Calculate the area of the plot
To find the area of the plot, we can rearrange the equation:
\[ A_p = 64 \times 8 = 512 \text{ m}^2 \]

### Step 5: Write the area of the plot in terms of length and breadth
The area of the rectangular plot can also be expressed as:
\[ A_p = l \times b = (2b) \times b = 2b^2 \]

### Step 6: Set the equations equal to each other
Now, we can set the two expressions for the area of the plot equal to each other:
\[ 2b^2 = 512 \]

### Step 7: Solve for \( b \)
To find \( b \), divide both sides by 2:
\[ b^2 = \frac{512}{2} = 256 \]
Now, take the square root of both sides:
\[ b = \sqrt{256} = 16 \text{ m} \]

### Step 8: Find the length of the plot
Now that we have the breadth, we can find the length using the relationship \( l = 2b \):
\[ l = 2 \times 16 = 32 \text{ m} \]

### Final Answer
The length of the rectangular plot is:
\[ \boxed{32 \text{ m}} \]

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