12. The map shows three bus stations at points A, B, and C, shown here. A tour from station A to the zoo to the port and back to A is 10 kilometers long. A tour from station B to the park to the zoo and back to B is 12 kilometers long. A tour from station C to the port and then the park and back to C is 13 kilometers long. Also, a tour from the zoo to the park to the port and then back to the zoo is 15 kilometers long. How long is the shortest tour from A to B to C, A to B to C, and then back to A? Okay, so the shortest tour from A to B to C to A is going to be this tour that basically traverses this perimeter of our map right here. So what we can do is we can sum up the lengths of the A, B, and C tours. Those do give us the tour of the map. They give us all of this, but they also give us this length in here. They give us this length and this length. So it gives us a little bit more than this whole perimeter length and that value is 10 plus 12 plus 13, which is 35. However, we also get this inner perimeter included, but guess what? They've given us the perimeter of the inner shape. So we subtract that from our sum to find the total length of this outer perimeter. So 10 plus 12 plus 13, this is tour A plus tour B plus tour C minus the inner tour gives us 20 and that is our answer B.

shortest tour

bus stations

routes

distances

perimeter