The length of a plot of land is four breadth. A playground measuring 1200 sq. metres occupies one – third of the total area of the plot. What is the length of the plot in metres?

Options

A. 90
B. 30
C. 20
D. None of these

Answer

To solve the problem step by step, let's define the variables and use the information given in the question.

### Step 1: Define Variables
Let the breadth of the plot be \( B \) meters. According to the problem, the length \( L \) of the plot is four times the breadth. Thus, we can express the length as:
\[ L = 4B \]

### Step 2: Calculate Total Area of the Plot
The total area \( A \) of the plot can be calculated using the formula for the area of a rectangle:
\[ A = L \times B \]
Substituting the expression for \( L \):
\[ A = (4B) \times B = 4B^2 \]

### Step 3: Relate the Area to the Playground
According to the problem, the playground occupies one-third of the total area of the plot, and the area of the playground is given as 1200 square meters. Therefore, we can set up the equation:
\[ \frac{1}{3} A = 1200 \]
Substituting the expression for \( A \):
\[ \frac{1}{3} (4B^2) = 1200 \]

### Step 4: Solve for \( B^2 \)
To eliminate the fraction, we can multiply both sides of the equation by 3:
\[ 4B^2 = 3600 \]
Now, divide both sides by 4:
\[ B^2 = 900 \]

### Step 5: Find the Value of \( B \)
Taking the square root of both sides gives us:
\[ B = \sqrt{900} = 30 \text{ meters} \]

### Step 6: Calculate the Length \( L \)
Now that we have the breadth, we can find the length using the relationship we defined earlier:
\[ L = 4B = 4 \times 30 = 120 \text{ meters} \]

### Conclusion
The length of the plot is \( 120 \) meters.

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