CAT 1999 Question Paper Question 33

Instructions

DIRECTIONS for the following two questions: These questions are based on the situation given below:

A rectangle PRSU, is divided into two smaller rectangles PQTU, and QRST by the line TQ. PQ=10cm, QR = 5 cm and RS = 10 cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are $$10 \sqrt{3}$$ cm apart.

Question 33

AB > AF > BF; CD > DE > CE; and BF = $$6\sqrt{5}$$ cm. Which is the closest pair of points among all the six given points?

Solution

The length of the diagonal of rectangle QRST is $$\sqrt{125}$$ cm = 11 cm approximately.

BF = $$6\sqrt5$$ cm > 12 cm

So, CE is definitely shorter than BF.

Option d) is the correct answer.

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