Below Diagram shows the shortest distance between Roshan's guest house and the park denoted by point P and Q respectively.
Now, Triangle "PSQ" is a right-angled triangle, so using Pythagoras Theorem: PQ2=PS2+SQ2 PQ2=(5)2+(12)2 PQ2=25+144 PQ2=169 PQ=√169 PQ=13. Hence, the correct answer is "13 km".