Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is

(a) 60
(b) 13 ✓ UPSC's answer
(c) 17
(d) 7

Why the answer is (b)

• Location B is directly north of A, and location C is directly east of A, forming a right-angled triangle with the right angle at A.

• The distance AB is given as 5 km, which serves as one leg of the triangle.

• The distance AC is given as 12 km, which serves as the other leg of the triangle.

• The shortest distance between B and C is the hypotenuse of this right-angled triangle.

• Using the Pythagorean theorem, the hypotenuse is calculated as √(5² + 12²) = √(25 + 144) = √169 = 13 km.

• Therefore, the shortest distance between locations B and C is 13 km, corresponding to option (b).

Why the other options are wrong

(a) 60: 60 km is the product of the two distances (5 × 12), not the hypotenuse of the right triangle.
(c) 17: 17 km is the sum of the two distances (5 + 12), which represents the path via A, not the direct shortest distance.
(d) 7: 7 km is the difference between the two distances (12 - 5), which is geometrically irrelevant to the hypotenuse calculation.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.