Question

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 100,000,000 people. What is the population density of Las Pythagoras?

Answer 1

320,000 people per km²

Explanation:

Since two angles are equal, their opposite lengths are also equal

Assuming it's a right ankle triangle,

Area = ½ × 25 × 25 = 312.5 km²

Population density:

100,000,000/312.5

320,000

Answer 2

320,000 people / km²

Explanation:

We need to find the area of the city first.

The area of a triangle is:
`A=(1)/(2) bh`, where b is the base and h is the height.

Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:

`A=(1)/(2) bh`

`A=(1)/(2) *25*25=312.5` km²

Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:

100,000,000 ÷ 312.5 = 320,000 people / km²