King Dashratha of Ayodhya had a rectangular plot of area `9792 m^(2) `. He divided it into 4 square shaped plots by fencing parallel fences to the breadth of the rectangular plot. All the four sons got each square shaped plot. However , same area of plot was still left which could not be formed as a square shaped. So, four more square shaped plots were formed by fencing parallel to the longer side of the original plot. The king gave one smaller square shaped plot to each of his wives and one of the smaller square shaped plot retained with himself and then nothing left to divide .
What are dimensions of the original plot ?

Options

A. 288 m, 34 m
B. 102 m , 96 m
C. 306 m , 32 m
D. 204 m , 48 m

Answer

To find the dimensions of the original rectangular plot owned by King Dashratha, we will follow these steps:

### Step 1: Understand the problem
The area of the rectangular plot is given as \(9792 \, m^2\). The plot is divided into square plots, and we need to find the dimensions (length and breadth) of the original rectangular plot.

### Step 2: Set up the equations
Let the side length of each square plot be \(x\). Since King Dashratha divided the rectangular plot into 4 square plots by fencing parallel to the breadth, the total breadth of the rectangular plot will be \(4x\).

After that, he formed 4 more square plots by fencing parallel to the length of the original plot. The total length of the rectangular plot will be \(17x\) (4 square plots of length \(x\) plus the original length).

### Step 3: Write the area equation
The area of the rectangular plot can be expressed as:
\[ \text{Area} = \text{Length} \times \text{Breadth} = (17x) \times (4x) = 68x^2 \]
Given that the area is \(9792 \, m^2\), we can set up the equation:
\[ 68x^2 = 9792 \]

### Step 4: Solve for \(x^2\)
To find \(x^2\), we divide both sides of the equation by 68:
\[ x^2 = \frac{9792}{68} \]
Calculating the right side:
\[ x^2 = 144 \]

### Step 5: Find \(x\)
Taking the square root of both sides gives:
\[ x = \sqrt{144} = 12 \, m \]

### Step 6: Find the dimensions of the rectangular plot
Now, we can find the length and breadth:
- Length \(L = 17x = 17 \times 12 = 204 \, m\)
- Breadth \(B = 4x = 4 \times 12 = 48 \, m\)

### Conclusion
The dimensions of the original rectangular plot are:
- Length = \(204 \, m\)
- Breadth = \(48 \, m\)