The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?

Options

A. 120m
B. 100m
C. 99m
D. 105m

Explanation

To solve the problem, we need to find the length of the diagonal of a square plot whose area is equal to that of a rectangular field with given dimensions.

### Step-by-Step Solution:

1. **Calculate the Area of the Rectangular Field:**
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given the length is 90 meters and the breadth is 80 meters, we can substitute these values into the formula:
\[ A = 90 \, \text{m} \times 80 \, \text{m} = 7200 \, \text{m}^2 \]

2. **Set the Area of the Square Equal to the Area of the Rectangle:**
Let the side of the square be \( s \). The area of the square is given by:
\[ A_{\text{square}} = s^2 \]
Since the area of the square is equal to the area of the rectangle, we have:
\[ s^2 = 7200 \, \text{m}^2 \]

3. **Calculate the Side Length of the Square:**
To find the side length \( s \), we take the square root of both sides:
\[ s = \sqrt{7200} \]

4. **Calculate the Diagonal of the Square:**
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = s\sqrt{2} \]
Substituting \( s = \sqrt{7200} \):
\[ d = \sqrt{7200} \times \sqrt{2} = \sqrt{7200 \times 2} = \sqrt{14400} \]
Now, calculate \( \sqrt{14400} \):
\[ d = 120 \, \text{m} \]

### Final Answer:
The length of the diagonal of the square plot is **120 meters**.