Emmett participated in a race. during the race, he ran 5 miles north and then ran 12 miles west. what is the shortest distance that emmett must travel to return to the starting point?

I'd suggest you sketch this situation.  If you did, you'd likely see right away that the shortest distance back to the starting point would be the hypotenuse of the right triangle whose legs are of lengths 5 miles and 12 miles.

Apply the Pythagorean Theorem to solve this.

The first one is 2/3the second is 1/160the third is 4/125