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Find the area of rectangle ABCD. I. The perimeter of rectangle ABCD is 4.5 times its breadth. II. The difference between the squares of the adjacent sides of rectangle ABCD is 5.4 times its breadth.

1. Neither statement (I) nor statement (II) by itself is sufficient to answer the question.
2. Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
3. Either statement (I) or statement (II) by itself is sufficient to answer the question.
4. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

Correct answer: Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

Solution

Statement I gives 2(l+b)=4.5b, which is one equation in two unknowns and is not sufficient alone. Statement II gives l^2-b^2=5.4b, which also is not sufficient alone. Together, they provide two equations that determine l and b, so the area can be found.

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