Each of these question have a questions followed by information given in three statements (1) (2) and (3). You have to study the question along with the information in three statements and decided that the information in which of the statement(s) is/are necessary to answer the question?
What is the area of the rectangular garden?
Perimeter of the garden is 220 metres
Length and the breadth of the garden are in the respective ratio of 7:4
Length is less than twice the breadth by 30 metres.

Options

A. Only 1 and 2
B. Only 1 and 3
C. 1 and either 2 or 3 only
D. Only 2 and 3

Answer

To determine the area of the rectangular garden, we need to analyze the information provided in the three statements.

### Step 1: Understand the Question
We need to find the area of a rectangular garden. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]

### Step 2: Analyze Statement (1)
**Statement (1):** Perimeter of the garden is 220 metres.

The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(\text{Length} + \text{Breadth}) \]
From this statement, we can set up the equation:
\[ 2(L + B) = 220 \]
Dividing both sides by 2 gives:
\[ L + B = 110 \]
This equation gives us a relationship between the length and breadth but does not provide their individual values.

### Step 3: Analyze Statement (2)
**Statement (2):** Length and the breadth of the garden are in the respective ratio of 7:4.

Let’s express the length and breadth in terms of a variable \( x \):
- Length \( L = 7x \)
- Breadth \( B = 4x \)

Now, substituting these into the equation from Statement (1):
\[ 7x + 4x = 110 \]
\[ 11x = 110 \]
\[ x = 10 \]

Now we can find the dimensions:
- Length \( L = 7 \times 10 = 70 \) metres
- Breadth \( B = 4 \times 10 = 40 \) metres

### Step 4: Calculate the Area
Now we can calculate the area:
\[ A = L \times B = 70 \times 40 = 2800 \text{ square metres} \]

### Step 5: Analyze Statement (3)
**Statement (3):** Length is less than twice the breadth by 30 metres.

This can be expressed as:
\[ L = 2B - 30 \]

We already have \( L + B = 110 \) from Statement (1). We can substitute \( L \) from this equation into the equation from Statement (3):
\[ (2B - 30) + B = 110 \]
\[ 3B - 30 = 110 \]
\[ 3B = 140 \]
\[ B = \frac{140}{3} \]
Now substituting back to find \( L \):
\[ L = 2 \times \frac{140}{3} - 30 = \frac{280}{3} - 30 = \frac{280 - 90}{3} = \frac{190}{3} \]

Now we can find the area:
\[ A = L \times B = \left(\frac{190}{3}\right) \times \left(\frac{140}{3}\right) = \frac{26600}{9} \text{ square metres} \]

### Conclusion
To find the area of the rectangular garden, we can conclude:
- Statement (1) is necessary to establish a relationship between length and breadth.
- Statement (2) is necessary to find the specific dimensions.
- Statement (3) is not necessary since we can find the area using Statements (1) and (2).

### Final Answer
Thus, the necessary statements to answer the question are **Statement (1) and Statement (2)**.