Amelia hikes 12 miles due east and then 5 miles due north what is the shortest distance in miles back

The shortest distance would be 13 miles

12 miles due east and then 5 miles due north; when you sketch east and north make angle of 90 degrees

so, use Pythagorean theorem to find the shortest distance which will be the hypotenuse

x%5E2=12%5E2%2B5%5E2

x%5E2=144%2B25

x%5E2=169

x=sqrt%28169%29

x=13

so, your answer is 13