The area of a rectangle measuring 6 m long is 30 `m^2`. Find the area of a square whose side is equal to the diagonal of rectangle.

Options

A. `61m^(2)`
B. `52m^(2)`
C. `42m^(2)`
D. `78m^(2)`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the given information
We have a rectangle with:
- Length (L) = 6 m
- Area (A) = 30 m²

### Step 2: Find the breadth of the rectangle
Using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
We can rearrange this to find the breadth (B):
\[ B = \frac{\text{Area}}{\text{Length}} = \frac{30 \, \text{m}^2}{6 \, \text{m}} = 5 \, \text{m} \]

### Step 3: Calculate the diagonal of the rectangle
To find the diagonal (D) of the rectangle, we can use the Pythagorean theorem:
\[ D = \sqrt{L^2 + B^2} \]
Substituting the values we found:
\[ D = \sqrt{6^2 + 5^2} = \sqrt{36 + 25} = \sqrt{61} \, \text{m} \]

### Step 4: Find the area of the square whose side is equal to the diagonal of the rectangle
The area (A_s) of a square is given by:
\[ A_s = \text{side}^2 \]
Since the side of the square is equal to the diagonal of the rectangle:
\[ A_s = D^2 = (\sqrt{61})^2 = 61 \, \text{m}^2 \]

### Conclusion
The area of the square whose side is equal to the diagonal of the rectangle is:
\[ \boxed{61 \, \text{m}^2} \]

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