The length of rectangular plot is thrice its breadth. If the area of the rectangular plot is 6075 sq. metres, what is its length?

Options

A. 145 meters
B. 130 meters
C. 75 meters
D. 45 metres

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variables
Let the breadth of the rectangular plot be denoted as \( B \). According to the problem, the length \( L \) is three times the breadth. Therefore, we can express the length as:
\[ L = 3B \]

### Step 2: Write the formula for the area of a rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times B \]
Substituting the expression for length, we have:
\[ A = (3B) \times B = 3B^2 \]

### Step 3: Set up the equation using the given area
We know the area of the rectangular plot is 6075 sq. meters. Therefore, we can set up the equation:
\[ 3B^2 = 6075 \]

### Step 4: Solve for \( B^2 \)
To isolate \( B^2 \), divide both sides of the equation by 3:
\[ B^2 = \frac{6075}{3} \]
Calculating the right side:
\[ B^2 = 2025 \]

### Step 5: Solve for \( B \)
Now, take the square root of both sides to find \( B \):
\[ B = \sqrt{2025} \]
Calculating the square root gives:
\[ B = 45 \, \text{meters} \]

### Step 6: Find the length \( L \)
Now that we have the breadth, we can find the length using the relationship \( L = 3B \):
\[ L = 3 \times 45 = 135 \, \text{meters} \]

### Final Answer
The length of the rectangular plot is:
\[ \boxed{135 \, \text{meters}} \]

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