Multiple choice

Directions: The following problem consists of a question and three statements numbered I, II and III. You have to determine which of the following statements is/are necessary to answer the question. What will be the area of the given right-angled triangle? I. One of the angles is 20o more than other angle. II. The perimeter of the triangle is 3 times its base. III. The length of its hypotenuse is 5 cm.

  1. Only II and III

  2. Only III

  3. Either II or III

  4. Both I and III

  5. The question cannot be answered even with the information given in all three statements.
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A Correct answer
AI explanation

The question provides three statements, but only statements II and III fix the triangle's shape and size. Knowing one angle is 20 degrees more than another simply gives the 30-60-90 angle ratio, which alone is insufficient for an absolute area. Combining the perimeter rule from statement II with the hypotenuse length from statement III perfectly determines the triangle's side lengths, so only statements II and III are necessary.

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