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.(Q. 1) 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?(Q. 2) 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.
Accepted Solution
A:
Scale :
Map 1 : Actual 1 cm : 2 km 1 cm : 200 000 cm | Convert 2km to 200 000cm
Answer: The scale is 1 : 200 000
Map 1 : Actual 1 cm : 200 000 cm (x8) : (x8) 8 cm : 1 600 000cm
1 600 000 cm = 16 km
Answer: The length of the actual trail is 16 km
Map 1 : Map 2 8cm : 6cm 1cm : 0.75 cm
Answer : The scale is 1 : 0.75
Map 1 : Map 2 1 : 0.075
3mm : 0.075 x 3 = 0.225mm
4mm : 0.075 x 4 = 0.3 mm
5mm : 0.075 x 5 = 0.375 mm
Answer: The side lengths are 0.225mm, 0.3 mm and 0.375 mm