Ajogger is going running in a rectangular park that is 28 meters by 96 meters. starting from where jogger's car is parked in the southeast corner, the jogger runs west along the width of the park and then north along the length. when the jogger reaches the northwest corner, she takes a shortcut straight back to her car. how far does the jogger run in all?

Pythagoras theorem in a right angle triangle the square of the hypotenuse is equal to the square of the other two sides.Total run by the jogger is 224 meters.

Given-

The length of the park is 96 meters.

The width of the park is 28 meters.

Now the jogger starts from the southeast corner from the park and go to the west direction till the last. After reaching the last point he takes a turn and run towards the north direction. Now he reached to the northwest direction and cover the length and width one time. Thus till now he total run by him is the sum of the length and width of the park,

Hence total distance covered by the jogged is 124 meters.

Now he takes shortcut. For this he run from northwest to the south east. This direction can be refer as the hypotenuse of the right angle triangle as shown in the attached image.

According to the Pythagoras theorem in a right angle triangle the square of the hypotenuse is equal to the square of the other two sides. Suppose hypotenuse is  x meter long. Thus,

Thus the shortest distance from the northwest to the southeast corner is 100 meter. The total run by the jogger is sum of the shortest distance to come and the run by him to reach southeast to the northwest corner earlier. Suppose total run by the jogger is l meters. Then,

Hence, total run by the jogger is 224 meters.

Learn more about the Pythagoras theorem here;

link

You can find the distance from the northwest corner back to the southeast corner by using the Pythagorean theorem:

See the attached picture: