What would be the length of the diagonal of a square plot whose area is equal to the area of a rectangular plot of 50 m length and 40.5m width?

Options

A. `45sqrt(2)` cm
B. 45 cm
C. 50 cm
D. `50sqrt(2)` cm

Answer

To find the length of the diagonal of a square plot whose area is equal to that of a rectangular plot with given dimensions, we can follow these steps:

### Step 1: Calculate the area of the rectangular plot.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
For the given rectangular plot:
- Length = 50 m
- Width = 40.5 m

Calculating the area:
\[ \text{Area} = 50 \, \text{m} \times 40.5 \, \text{m} = 2025 \, \text{m}^2 \]

### Step 2: Set the area of the square plot equal to the area of the rectangular plot.
Let the side of the square plot be \( s \). The area of a square is given by:
\[ \text{Area} = s^2 \]
Setting the area of the square equal to the area of the rectangle:
\[ s^2 = 2025 \]

### Step 3: Solve for the side length \( s \) of the square.
To find \( s \), take the square root of both sides:
\[ s = \sqrt{2025} \]
Calculating the square root:
\[ s = 45 \, \text{m} \]

### Step 4: Calculate the length of the diagonal of the square.
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = s \sqrt{2} \]
Substituting the value of \( s \):
\[ d = 45 \, \text{m} \times \sqrt{2} \]

### Step 5: Final calculation of the diagonal.
Using the approximate value of \( \sqrt{2} \approx 1.414 \):
\[ d \approx 45 \times 1.414 \approx 63.64 \, \text{m} \]

Thus, the length of the diagonal of the square plot is approximately:
\[ \boxed{63.64 \, \text{m}} \]