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 32

Which of the following statements is necessarily true?

Solution

The sides of the rectangle PRSU are PR = 15 cm and
RS = 10 cm. The maximum possible distance i.e. diagonal will be $$\sqrt{325}=5\times\sqrt(13)$$ cm. 
The maximum possible distance among C, D and E is $$5\times\sqrt(5)$$.
The maximum possible distance among A, B and F is $$5\times\sqrt(8)$$.  
The minimum distance between points formed by taking one from A, B, F and C,D, E is $$10\times\sqrt(3)=5\times\sqrt(12)$$cm.
wkt, among all 6 points, the closest pair among them has to be less than $$5\times\sqrt(5)$$
Hence, this pair cannot be the closest among the 6 pair of points. So, the statement in option a) should be true.


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