Question: What is the area of the triangle inscribed in a semi-circle with the diameter as the base?<br>Statement-I:<br>The diameter of semi-circle is 20 cm.<br>Statement-II:<br>Two shorter sides of the triangle are 12 cm and 16 cm.

Consider the following for the next ten (10) items that follow :<br>Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.<br>Mark option (b) if the question can be answered by using either statement alone.<br>Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone.<br>Mark option (d) if the question cannot be answered even by using both the statements together.

  1. A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone ✓
  2. B. The question can be answered by using either statement alone
  3. C. The question can be answered by using both the statements together, but cannot be answered using either statement alone
  4. D. The question cannot be answered even by using both the statements together

Correct Answer: A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

Explanation

A triangle inscribed in a semicircle with the diameter as its base is a right-angled triangle. Statement-I provides the hypotenuse (20 cm), but the legs are unknown, so area cannot be found. Statement-II provides the two legs (12 cm and 16 cm), allowing the area to be calculated directly as \frac{1}{2} \times 12 \times 16 = 96 sq cm. Thus, Statement-II alone is sufficient.

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