The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 kilometers long. The population in Las Pythagoras is 100,000 people.

What is the population density of Las Pythagoras?
Round your answer, if necessary, to the nearest integer.
people per square kilometer

Step 1 ：The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 kilometers long. The population in Las Pythagoras is 100,000 people.

Step 2 ：The population density is calculated by dividing the total population by the total area. In this case, the area of the city is the area of an isosceles right triangle, which is calculated by the formula \(\frac{1}{2} \times \text{base} \times \text{height}\). Since the base and height are both 25 kilometers, the area is \(\frac{1}{2} \times 25 \times 25 = 312.5\) square kilometers.

Step 3 ：The population density is then \(\frac{100,000}{312.5} = 320\) people per square kilometer. However, since the question asks to round to the nearest integer, the final answer should be rounded to 320.

Step 4 ：Final Answer: The population density of Las Pythagoras is \(\boxed{320}\) people per square kilometer.