The length of plot is 4 times its breadth. A playground measuring `12m^2` occupies one third of the total area of the plot in metres. What is the length of plot?

Options

A. 9m
B. 8m
C. 12m
D. None of these

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the breadth of the plot be \( b \) meters. According to the question, the length \( l \) of the plot is 4 times its breadth. Therefore, we can express the length as:
\[ l = 4b \]

### Step 2: Calculate the Area of the Plot
The area \( A \) of the plot can be calculated using the formula for the area of a rectangle:
\[ A = l \times b = (4b) \times b = 4b^2 \]

### Step 3: Relate the Playground Area to the Plot Area
We know that the playground occupies \( 12 \, m^2 \) and that it is one third of the total area of the plot. Therefore, we can write:
\[ \frac{1}{3} A = 12 \]
Substituting the area of the plot from Step 2:
\[ \frac{1}{3} (4b^2) = 12 \]

### Step 4: Solve for \( b^2 \)
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 4b^2 = 36 \]
Now, divide both sides by 4:
\[ b^2 = 9 \]

### Step 5: Find the Value of \( b \)
Taking the square root of both sides gives us:
\[ b = 3 \, \text{meters} \]

### Step 6: Calculate the Length of the Plot
Now that we have the breadth, we can find the length of the plot using the relationship defined in Step 1:
\[ l = 4b = 4 \times 3 = 12 \, \text{meters} \]

### Final Answer
The length of the plot is:
\[ \text{Length of the plot} = 12 \, \text{meters} \]

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