7-3. A secret object is a rectangle measuring $200 \times 300$ meters. Outside the object, there is a guard at each of the four corners. An intruder approached the perimeter of the secret object from the outside, and all the guards ran to him along the shortest paths along the external perimeter (the intruder remained in place). Three of the guards ran a total of 850 meters to reach the intruder. How many meters did the fourth guard run to reach the intruder?
Answer: 150.

Solution. Note that no matter where the violator is, two guards in opposite corners will run a distance equal to half the perimeter in total.
![](https://cdn.mathpix.com/cropped/2024_05_06_7d113eccc6d3ed32fb40g-12.jpg?height=336&width=1746&top_left_y=212&top_left_x=160)

Therefore, all four guards will run a total distance equal to the perimeter (two in diagonally opposite corners will run a total of half the perimeter, and the other two will also run half the perimeter). Therefore, the fourth guard will run a distance that complements 850 to the perimeter, which is 1000, i.e., 150 meters.