Question

a jogger ran 4 miles east and then 8 miles north. what is the shortest distance the jogger must travel to return to their starting point? express your answer as a simplified square root.
4√5 miles
12 miles
4√3 miles
10√5 miles

Explanation:

Step1: Identify movement directions

The jogger runs 4 miles east (horizontal leg) and 8 miles north (vertical leg).

Step2: Apply Pythagorean theorem

Let $a = 4$, $b = 8$. The shortest distance $d$ is $\sqrt{a^2 + b^2}$.

Step3: Calculate the distance

$$d = \sqrt{4^2 + 8^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}$$

Answer:

A. $4\sqrt{5}$ miles