Final answer:
The answer is 13 miles. To find the shortest distance back to Nevin's starting point after running north and then east, we use the Pythagorean theorem to calculate the hypotenuse of a right-angled triangle.
Step-by-step explanation:
The student's question involves finding the shortest distance Nevin must travel to return to her starting point after running 12 miles north and then 5 miles east.
This scenario can be represented as a right-angled triangle where the legs are the distances traveled north and east, and the hypotenuse is the shortest distance back to the starting point.
To solve this, we use the Pythagorean theorem which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this scenario, a = 12 miles and b = 5 miles. Plugging these values into the Pythagorean theorem:
c² = a² + b²
c² = 12² + 5²
c² = 144 + 25
c² = 169
Now we find c by taking the square root of both sides:
c = √169
c = 13 miles
Therefore, the shortest distance that Nevin must travel to return to her starting point is 13 miles.