At the beginning of practice, the coach divides the athletes into two groups. She asks one group to run around the gym 4 times, the other group to run back and forth along the diagonal of the gym 5 times. She claims that the two paths are equal in length.

Construct examples of gyms for which one of the paths is longer than the other, and vice versa.

Write expressions that describe the length of the path according to each of the two methods.

What should be the shape of the gym if the coach's claim is correct?