Question

What is the height of a right-angled triangle?
Statement I. The area of the right-angled triangle is equal to the area of a rectangle whose breadth is 15 m.
Statement II. The length of the rectangle is 12 m.

• 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 the question.
• B. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
• C. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
• D. If the data even in both statements I and II together are not sufficient to answer the question.

Hint:

When solving for unknown dimensions in geometric shapes, always ensure that all necessary values (e.g., base and height) are known or can be derived from the given information.

Answer 1

The Correct Option is D

- From Statement I, we know that the area of the right-angled triangle is equal to the area of the rectangle. The area of the rectangle is given by \( \text{Area} = \text{length} \times \text{breadth} \). However, we do not know the base of the triangle, which is necessary to find the height.
- Statement II provides the length of the rectangle, but we still do not know the base of the triangle, which is necessary to calculate the height.
Hence, even combining both statements, we cannot determine the height of the triangle. Therefore, the correct answer is (D).