The runner's resulting displacement is approximately 16.97 km.
To find the runner's resulting displacement, we can use the Pythagorean theorem. The distance traveled north is 12 km, and the distance traveled east is also 12 km. We can treat these distances as the two legs of a right triangle. The resulting displacement is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can calculate the resulting displacement:
a^2 + b^2 = c^2
12^2 + 12^2 = c^2
144 + 144 = c^2
288 = c^2
c = sqrt(288)
c ≈ 16.97
Therefore, the runner's resulting displacement is approximately 16.97 km.