Scenario: Maps & Models - Learn to work with scale factors and similar figures!
A building model is made at a scale of 1:200. If the model is 15 cm tall, what is the actual height of the building?
Solution: 15 cm ÷ (1/200) = 15 × 200 = 3000 cm = 30 m
The actual building is 30 meters tall.
Scale Factor Definition: The ratio of any two corresponding lengths in similar figures.
Scale 1:200 means 1 unit on the model = 200 units in real life.
Two similar triangles have corresponding sides in the ratio 3:5. If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?
Solution: 24 cm × (5/3) = 40 cm
The larger triangle has a perimeter of 40 cm.
A person 1.6 m tall casts a shadow 2 m long. A tree casts a shadow 10 m long. How tall is the tree?
Solution using similar triangles:
Person height : Person shadow = Tree height : Tree shadow
1.6 m : 2 m = x : 10 m
x = (1.6 × 10) ÷ 2 = 8 m
A car model is 1:24 scale. If the model is 7.5 cm long, how long is the real car?
Your solution:
On a map with scale 1:50,000, two cities are 8 cm apart. What is the actual distance?
Your solution: