The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the legth of the diagonal of a square garden having the same area as that of the rectangular garden :

Options

A. `2sqrt(30)m`
B. `sqrt(13)m`
C. 13 m
D. `8sqrt(15)m`

Answer

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

### Step 1: Calculate the area of the rectangular garden.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Substituting the given values:
\[ \text{Area} = 12 \, \text{m} \times 5 \, \text{m} = 60 \, \text{m}^2 \]

### Step 2: Set the area of the square garden equal to the area of the rectangular garden.
Let the side of the square garden be \( x \). The area of a square is given by:
\[ \text{Area} = x^2 \]
Since the area of the square garden is equal to the area of the rectangular garden:
\[ x^2 = 60 \]

### Step 3: Solve for \( x \).
To find \( x \), take the square root of both sides:
\[ x = \sqrt{60} \]
This can be simplified:
\[ x = \sqrt{4 \times 15} = 2\sqrt{15} \]

### Step 4: Calculate the length of the diagonal of the square garden.
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = x\sqrt{2} \]
Substituting the value of \( x \):
\[ d = 2\sqrt{15} \times \sqrt{2} = 2\sqrt{30} \]

### Final Answer:
The length of the diagonal of the square garden is:
\[ d = 2\sqrt{30} \, \text{meters} \]

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