Question: The diagonals of a rhombus ABCD are in the ratio 5:12. Is one of the diagonals equal to side of the rhombus? Statement I: The sum of the diagonals = 34 cm. Statement II: The length of a side = 13 cm.

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?

  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 can be answered even without using any of the Statements ✓

Correct Answer: D. The Question can be answered even without using any of the Statements

Explanation

Let diagonals be 5x and 12x. The side of the rhombus is \sqrt{(2.5x)^2 + (6x)^2} = \sqrt{42.25x^2} = 6.5x. Clearly, 6.5x equals neither 5x nor 12x. Thus, the answer is 'No', definitively derived without requiring either statement.

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