Question

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.

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?
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:

Answer 1

The scale factor of the map to the real trail is 1cm from the map is 2km from the real trail. And the actual trail length is 16km.

8cm x 2km = 16km

b) The scale factor from the first map to the second map is 1 cm from the map to 2.67 km from the actual route.

16km/6cm = 2.67km

The side lengths of the landmark on the second map are 3x = 9/4, 4x = 3, and 5x = 15/4.

3x = 9/4

x = 9 / 4 x 3 = 9/12

x = 9/12

9/3 = 3 12/3 = 4

x = 3/4

4x= 3

4/4 = 4 4/3 = 3

x = 3/4

5x = 15/4

x = 15 / 4 x 3 = 15/20

x = 15/20

15/3 = 5 20/4 = 5

x = 3/4

Answer 2

first calculate the length of the actual trail
trail = 8 cm ( 2 km / 1 cm )
trail = 16 km
so the scale factor of the second map is:
scale = 16 km / 6 cm
scale = 2.67 km / 1 cm
the scale on the 2nd map is 1 cm represent 2.67 km in the actual trail