The length of rectangular plotis 144 m and its area is same as that of a square plot with one of its sides being 84 m. The width of the plot is:

Options

A. 7m
B. 49m
C. 14m
D. None of these

Answer

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

### Step 1: Calculate the area of the square plot.
The area of a square is given by the formula:
\[ \text{Area} = \text{side} \times \text{side} \]
Given that the side of the square plot is 84 m, we can calculate its area:
\[ \text{Area of square} = 84 \, \text{m} \times 84 \, \text{m} = 7056 \, \text{m}^2 \]

### Step 2: Set up the equation for the area of the rectangular plot.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
Let the width of the rectangular plot be \( B \). The length is given as 144 m. Therefore, we can write:
\[ \text{Area of rectangle} = 144 \, \text{m} \times B \]

### Step 3: Set the areas equal to each other.
Since the area of the rectangular plot is the same as that of the square plot, we can set the two areas equal:
\[ 144 \, \text{m} \times B = 7056 \, \text{m}^2 \]

### Step 4: Solve for the width \( B \).
To find \( B \), we can rearrange the equation:
\[ B = \frac{7056 \, \text{m}^2}{144 \, \text{m}} \]
Now, we perform the division:
\[ B = 49 \, \text{m} \]

### Conclusion
The width of the rectangular plot is \( 49 \, \text{m} \).

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