The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. metre, what is the breadth of the rectangular plot?

Options

A. 88 metres
B. 104 metres
C. 153 metres
D. 51 metres

Answer

To find the breadth of the rectangular plot, we can follow these steps:

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:
\[ L = 3b \]

2. **Use the Area Formula**:
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times b \]
We know from the problem that the area is 7803 square meters. Substituting the expression for \( L \) into the area formula gives:
\[ A = (3b) \times b = 3b^2 \]
Setting this equal to the given area:
\[ 3b^2 = 7803 \]

3. **Solve for \( b^2 \)**:
To isolate \( b^2 \), divide both sides of the equation by 3:
\[ b^2 = \frac{7803}{3} \]
Calculating the right-hand side:
\[ b^2 = 2601 \]

4. **Find \( b \)**:
To find \( b \), take the square root of both sides:
\[ b = \sqrt{2601} \]
Calculating the square root gives:
\[ b = 51 \]

5. **Conclusion**:
The breadth of the rectangular plot is:
\[ \text{Breadth} = 51 \text{ meters} \]