Question

Answer the questions based on the following information:
A rectangle PRSU is divided into two smaller rectangles PQTU, and QRST by the line TQ.PQ = 10cm. QR = 5 cm and Rs = 10cm. 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,E), (B,C), (B,D), (B,E) are 10√3 cm apart.
Which of the following statements is necessarily true?

• A. The closest pair of points among the six given points cannot be (F, C).
• B. Distance between A and B is greater than that between F and C.
• C. The closest pair of points among the six given points is (C, D), (D, E) or (C, E).
• D. None of the above

Answer 1

The correct option is A The closest pair of points among the six given points cannot be (F, C).

The diagonal length of a rectancle PUSR = $5\sqrt{13}$ = 18 (approx)

Among given eight pairs the shortest distance = $10\sqrt{3}$

So, the six points A, B, F, C, D and E are near corner of rectangle PUSR.

So, (F,C) cannot be the shortest distance.