Given below in each question there are two statements (I) and (II). You must determine, which statement is enough to give the answer of question. Also, there are five alternatives given, you have to choose one alternative as your answer of the questions:
What is area of the rectangle.
I. Length is 50% more than breadth.
II. Perimeter of square is 48 cm and breadth of rectangle is equal to side of square.

Options

A. A)only statement I
B. B)Only statement II
C. C)Both I and Il together
D. D)Either I or Il alone

Answer

To solve the problem of finding the area of the rectangle based on the given statements, let's analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** Length is 50% more than breadth.

Let:
- Breadth = B
- Length = L

From the statement, we can express the length in terms of the breadth:
\[ L = B + 0.5B = 1.5B \]

Now, we know the relationship between length and breadth, but we do not have specific values for either. Therefore, we cannot calculate the area (Area = Length × Breadth) without knowing the actual dimensions.

**Conclusion for Statement I:** This statement alone is **not sufficient** to determine the area of the rectangle.

### Step 2: Analyze Statement II
**Statement II:** Perimeter of square is 48 cm and breadth of rectangle is equal to the side of the square.

The perimeter of a square is given by:
\[ \text{Perimeter} = 4 \times \text{side} \]

Setting the perimeter equal to 48 cm:
\[ 4 \times \text{side} = 48 \]
\[ \text{side} = \frac{48}{4} = 12 \text{ cm} \]

Since the breadth of the rectangle is equal to the side of the square:
\[ B = 12 \text{ cm} \]

Now we have the breadth, but we still need the length to find the area.

**Conclusion for Statement II:** This statement alone is **not sufficient** to determine the area of the rectangle.

### Step 3: Combine Statements I and II
Now, let's combine both statements to find the area.

From Statement II, we have:
- Breadth (B) = 12 cm

From Statement I, we have:
- Length (L) = 1.5B = 1.5 × 12 cm = 18 cm

Now we can calculate the area of the rectangle:
\[ \text{Area} = L \times B = 18 \text{ cm} \times 12 \text{ cm} = 216 \text{ cm}^2 \]

### Final Conclusion
Both statements together provide sufficient information to calculate the area of the rectangle.

### Answer
The correct option is **C: Both I and II together are sufficient.**

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