Amelia hikes 12 miles due east and then 5 miles due north. What is the shortest distance in miles back to where she began?

Question

(1 point)
Responses

13
13

11
11

6
6

4

Answer 1

To find the shortest distance back to where Amelia began, we can use the Pythagorean theorem.

The distance Amelia traveled east and north can be seen as the legs of a right triangle.

The distance traveled east is 12 miles and the distance traveled north is 5 miles.

So, the shortest distance back to where she began is the hypotenuse of the right triangle formed by these two distances.

Using the Pythagorean theorem, we have:

Shortest distance = √(12^2 + 5^2) = √(144 + 25) = √169 = 13

Therefore, the shortest distance in miles back to where Amelia began is 13 miles.

The correct answer is 13.