Question

1. Pia printed two maps of a walking trail. The length of the trail on the first map is 8 cm. The length of the trail on the second map is 6 cm.
(a) 1 cm on the first map represents 2 km on the actual trail. What is the scale factor from the map to the actual trail? What is the length of the actual trail?
(b) A landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm. What is the scale factor from the first map to the second map? What are the side lengths of the landmark on the second map? Show your work.

Answer 1

Given:
1st map = 8 cm
2nd map = 6 cm

1 cm in the map is equal to 2 km on the actual trail. 
8 cm * 2km/1cm = 16 km is the actual length of the trail in the first map
6 cm * 2km/1cm = 12 km is the actual length of the trail in the second map.

I'm not sure on how to get the scale factor from the map to the actual trail. I'm confused if I had to consider cm and km because 1km is equal to 100,000 cm. 

Proportion of the second  map to the first map is 6/8

6/8 = x/3 → 6*3 = 8x → 18/8 = x → 2.25
6/8 = x/4 → 6*4 = 8x → 24/8 = x → 3
6/8 = x/5 → 6*5 = 8x → 30/8 = x →3.75


The side measure of the triangle in the second map is only 75% of the side measure of the triangle in the  first map.