1. A map scale is 1 cm represents 5 km. What real distance is shown by 7 cm?

Answer: 35 km.

2. A 12 m wall is drawn as 6 cm. Find the scale in simplest form.

Answer: Scale $1:200$ after converting 12 m to 1200 cm.

3. A map uses scale $1:50\,000$. What real distance does 4 cm represent in km?

Answer: 2 km.

4. A 15 km road is 3 cm on a map. How many cm represent 1 km?

Answer: 0.2 cm per km.

5. A 4.5 m table is drawn at scale $1:30$. Find its drawing length in cm.

Answer: 15 cm.

6. Two towns are 8.2 cm apart on a map with scale $1:250\,000$. Find the real distance in km.

Answer: 20.5 km.

7. A model is 18 cm long; the real object is 2.7 m long. Write model:real scale.

Answer: Convert to 270 cm: scale $1:15$.

8. On a scale drawing, a path measures 6 cm at scale $1:10\,000$. Find its real length in metres.

Answer: 600 m.

9. A square side is enlarged by scale factor 3. What is the new side if it began at 4 cm?

Answer: 12 cm.

10. A map distance is 3.6 cm at scale $1:75\,000$. Find the real distance in km.

Answer: 2.7 km.

11. Why must map and real lengths use the same units before forming a scale ratio?

Answer: A ratio compares like quantities; matching units prevents a factor-of-100 or factor-of-1000 error.

12. A room is 5.4 m wide. Find its width on a plan at scale $1:60$.

Answer: 9 cm.

13. A map scale is $1:25\,000$. A route is 4 cm long on the map. Work out its real length in kilometres. Which unit conversion is needed, and why?

Answer: 1 km. First convert the map length to 100,000 cm, then convert centimetres to kilometres.