Area of a rectangle is equal to the area of a right angled triangle. What is the length of the rectangle ?
I. The base of the triangle is 40 cms.
II. The height of the triangle is 50 cms.

Options

A. if the data in Statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer to question.
B. if the data in statement Ii alone are sufficient to answer the questin, while the data in statemetn I alone are not suffcient to answer the question.
C. if the data wither in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data event in both the statements I and II together are necessary to answer the question.

Explanation

To solve the problem, we need to find the length of a rectangle given that its area is equal to the area of a right-angled triangle. We will analyze the information provided in the statements to determine if they are sufficient to find the length of the rectangle.

### Step-by-Step Solution:

1. **Understanding the Areas**:
- The area of a rectangle is given by the formula:
\[ \text{Area of Rectangle} = \text{Length} \times \text{Breadth} \]
- The area of a right-angled triangle is given by the formula:
\[ \text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

2. **Setting Up the Equation**:
- According to the problem, the area of the rectangle is equal to the area of the triangle:
\[ \text{Length} \times \text{Breadth} = \frac{1}{2} \times \text{Base} \times \text{Height} \]

3. **Using Statement I**:
- Statement I tells us that the base of the triangle is 40 cm.
- Substituting this into the area of the triangle:
\[ \text{Area of Triangle} = \frac{1}{2} \times 40 \times \text{Height} \]
- We still need the height to calculate the area of the triangle and thus the area of the rectangle.

4. **Using Statement II**:
- Statement II tells us that the height of the triangle is 50 cm.
- Substituting this into the area of the triangle:
\[ \text{Area of Triangle} = \frac{1}{2} \times 40 \times 50 \]
- Calculating this gives:
\[ \text{Area of Triangle} = \frac{1}{2} \times 40 \times 50 = 1000 \text{ cm}^2 \]

5. **Finding the Area of the Rectangle**:
- Now we know that the area of the rectangle is also 1000 cm²:
\[ \text{Length} \times \text{Breadth} = 1000 \]
- However, we have two variables (Length and Breadth) and only one equation. Therefore, we cannot uniquely determine the length of the rectangle without knowing the breadth.

6. **Conclusion**:
- Both statements together provide the necessary information to calculate the area of the triangle, which is equal to the area of the rectangle. However, since we have two variables and only one equation, we cannot find a unique solution for the length of the rectangle.

### Final Answer:
The information provided in both statements is insufficient to determine the length of the rectangle.

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