The lengths of two longer sides of the triangle \Delta are 25 cm and 24 cm.<br>Question: What is the length of the <strong>SHORTEST</strong> side?<br>Statement I: The angles of \Delta are in the ratio 1:2:3.<br>Statement II: The length of the perpendicular drawn on the longest side of \Delta from its opposite vertex is 6.72 cm.

For the next ten (10) items that follow:<br>Each item contains a Question followed by two Statements. Answer each item using the following instructions:

  1. A. Choose this option if the Question can be answered by one of the Statements alone but not by the other. ✓
  2. B. Choose this option if the Question can be answered by either Statement alone.
  3. C. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
  4. D. Choose this option if the Question cannot be answered even by using both Statements together.

Correct Answer: A. Choose this option if the Question can be answered by one of the Statements alone but not by the other.

Explanation

Statement I defines a 30-60-90 triangle, but such a triangle cannot have consecutive long sides of 24 and 25 (hypotenuse 25 means legs are 12.5 and 12.5\sqrt{3}). Statement II gives an altitude h_c = 6.72 on the hypotenuse 25. Using geometric properties, the third side can be calculated as 7 cm (a 7-24-25 right triangle). Thus, only Statement II is sufficient and valid.

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