Use scale drawings and enlarged drawings to find actual distances and heights.
📘 Example ① (Scale Drawing)
On a map with a scale of 1:25000, what actual distance in km is represented by 4cm?
Answer: 4cm × 25000 = 100000cm = 1km
On a map with a scale of 1:25000, what actual distance in km is represented by 4cm?
Answer: 4cm × 25000 = 100000cm = 1km
📘 Example ② (Using Shadows)
A 2m-high pole casts a 1.5m shadow. At the same time, a tree casts a 6m shadow. Find the height of the tree.
Answer: Pole:tree = 1.5:6 = 1:4 (ratio of shadows). Height of tree = 2 × 4 = 8m
A 2m-high pole casts a 1.5m shadow. At the same time, a tree casts a 6m shadow. Find the height of the tree.
Answer: Pole:tree = 1.5:6 = 1:4 (ratio of shadows). Height of tree = 2 × 4 = 8m
💡 Key Point
- Scale = length on the map / actual length
- At the same time, the ratio of shadow lengths equals the ratio of heights (using similarity).
Practice Problems
- On a map with a scale of 1:50000, what actual distance in km is represented by 3cm?
Answer and Explanation
- Answer: 1.5km. 3 × 50000 = 150000cm = 1500m = 1.5km.