Question

A park has two jogging tracks. The tracks are similar triangles. If Chang jogs one lap around the inside track, how far does he jog?

a. 675 m
b. 845 m
c. 1183 m
d. 1277 m

Answer 1

Chang jogs a distance of 675 m around the inside track.

Step-by-step explanation:

The distance that Chang jogs around the inside track can be found by multiplying the length of one side of the inside track by the number of sides. Since the inside track is a triangle and the tracks are similar triangles, we need to determine the ratio of the corresponding sides of the inside and outside tracks.

Let's say the length of one side of the inside track is x. According to the given information, the length of one side of the outside track is 3x. Therefore, the ratio of the corresponding sides is 1:3.

Since the inside track is a triangle, it has 3 sides. So the distance that Chang jogs around the inside track is 3 times the length of one side: 3x.

Now, we just need to substitute the value of x with the given information. If we take the length of one side of the outside track as 675 m, then the length of one side of the inside track would be 225 m. Therefore, the distance that Chang jogs around the inside track is:

3 * 225 = 675 m.