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 is the ratio of the area of larger square shaped plot to the area of the smaller square shaped plot ?

Options

A. A. `17:1`
B. B. `25:9`
C. C. `16:1`
D. D. can't be determined

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the dimensions of the rectangular plot
The area of the rectangular plot is given as \( 9792 \, m^2 \). We will denote the breadth of the rectangular plot as \( b \) and the length as \( l \). The area can be expressed as:
\[ l \times b = 9792 \]

### Step 2: Divide the plot into square-shaped plots
King Dashratha divides the rectangular plot into 4 square-shaped plots by fencing parallel to the breadth. Each square-shaped plot will have a side length of \( x \). Therefore, the total breadth occupied by the four square plots is:
\[ 4x = b \]

### Step 3: Calculate the area of the smaller square-shaped plots
The area of each smaller square-shaped plot is given by:
\[ \text{Area of smaller square} = x^2 \]

### Step 4: Determine the dimensions of the larger square-shaped plot
Since the remaining area after dividing into four smaller squares is still rectangular, we can find the length of the larger square-shaped plot. The length of the larger square plot will be equal to the breadth of the rectangular plot, which is \( b \), and its side length will also be equal to \( 4x \) (since it is a square):
\[ \text{Area of larger square} = (4x)^2 = 16x^2 \]

### Step 5: Find the ratio of the area of the larger square to the area of the smaller square
Now, we can find the ratio of the area of the larger square-shaped plot to the area of the smaller square-shaped plot:
\[ \text{Ratio} = \frac{\text{Area of larger square}}{\text{Area of smaller square}} = \frac{16x^2}{x^2} \]
This simplifies to:
\[ \text{Ratio} = 16 \]

### Final Answer
Thus, the ratio of the area of the larger square-shaped plot to the area of the smaller square-shaped plot is:
\[ \text{Ratio} = 16 : 1 \]

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