The following questions are accompanied by two statements (A), (B). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
What is the perimeter of a rectangular plot?
A. The area of the plot is 2400 sq.metres and diagonal length of the garden is 50 metres.
B. Length is 50% more than the breadth of the plot.

Options

A. Statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the questions.
B. Statement B alone is sufficient to answer the question but statement A alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the questions.
D. Either statement A or statement B by itself is sufficient to answer the question.

Answer

To determine the perimeter of a rectangular plot based on the given statements, we can analyze each statement step by step.

### Step 1: Understand the Formula for Perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
where \( L \) is the length and \( B \) is the breadth of the rectangle.

### Step 2: Analyze Statement A
Statement A provides:
- The area of the plot is 2400 sq. metres.
- The diagonal length of the plot is 50 metres.

From the area, we know:
\[ L \times B = 2400 \quad \text{(1)} \]

From the diagonal, by using the Pythagorean theorem:
\[ L^2 + B^2 = 50^2 = 2500 \quad \text{(2)} \]

### Step 3: Solve the Equations from Statement A
From equation (1), we can express \( L \) in terms of \( B \):
\[ L = \frac{2400}{B} \]

Substituting \( L \) in equation (2):
\[ \left(\frac{2400}{B}\right)^2 + B^2 = 2500 \]

Expanding this gives:
\[ \frac{5760000}{B^2} + B^2 = 2500 \]

Multiplying through by \( B^2 \) to eliminate the fraction:
\[ 5760000 + B^4 = 2500B^2 \]

Rearranging gives us a quartic equation:
\[ B^4 - 2500B^2 + 5760000 = 0 \]

Let \( x = B^2 \), then we have:
\[ x^2 - 2500x + 5760000 = 0 \]

Using the quadratic formula:
\[ x = \frac{2500 \pm \sqrt{2500^2 - 4 \times 5760000}}{2} \]

Calculating the discriminant:
\[ 2500^2 - 4 \times 5760000 = 6250000 - 23040000 = -16790000 \]

Since the discriminant is negative, we can conclude that there are no real solutions for \( B \) and \( L \) based on the conditions provided in Statement A. However, we can still derive the perimeter once we have valid \( L \) and \( B \).

### Step 4: Analyze Statement B
Statement B states:
- The length is 50% more than the breadth.

This can be expressed as:
\[ L = B + 0.5B = 1.5B \quad \text{(3)} \]

Using equation (1) with equation (3):
\[ 1.5B \times B = 2400 \]
\[ 1.5B^2 = 2400 \]
\[ B^2 = \frac{2400}{1.5} = 1600 \]
\[ B = 40 \]

Substituting back to find \( L \):
\[ L = 1.5 \times 40 = 60 \]

Now we can find the perimeter:
\[ P = 2(L + B) = 2(60 + 40) = 2 \times 100 = 200 \]

### Conclusion
- Statement A alone is sufficient to find the perimeter since it provides the area and diagonal.
- Statement B alone is also sufficient to find the perimeter since it provides a direct relationship between length and breadth.

Thus, the answer is that **Statement A alone is sufficient** to answer the question.