To determine the total distance of the jogging trail, we need to calculate the distance along each segment of the trail and then add these distances together.
1. The trail first covers a distance of 600 meters going west.
2. Then, the trail covers a distance of 800 meters going north.
3. Finally, the trail heads back to the starting point, forming a right triangle.
Since the trail forms a right triangle, we use the Pythagorean theorem to find the length of the hypotenuse, which is the third side of the triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse [tex]\( c \)[/tex] is equal to the sum of the squares of the other two sides [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
In this case, [tex]\( a = 600 \)[/tex] meters and [tex]\( b = 800 \)[/tex] meters. We substitute these values into the theorem:
[tex]\[ 600^2 + 800^2 = c^2 \][/tex]
Solving for [tex]\( c \)[/tex]:
[tex]\[ 360000 + 640000 = c^2 \][/tex]
[tex]\[ 1000000 = c^2 \][/tex]
[tex]\[ c = \sqrt{1000000} \][/tex]
[tex]\[ c = 1000 \text{ meters} \][/tex]
So, the length of the hypotenuse is 1000 meters.
Now, we add all three segments of the trail to get the total distance:
[tex]\[ \text{Total distance} = 600 \text{ meters} + 800 \text{ meters} + 1000 \text{ meters} \][/tex]
[tex]\[ \text{Total distance} = 2400 \text{ meters} \][/tex]
Thus, the total distance of the jogging trail is 2400 meters.
So, the correct answer is:
O 2,400 m
