How to Solve Scale Drawing Problems

What Is a Scale?

A scale tells you the ratio between a drawing (or model) and real life.
Example: 1 inch = 10 feet means every inch on the drawing represents 10 feet in reality.

How to Solve Scale Problems

A map has a scale of 1 cm = 25 km. Two cities are 4 cm apart on the map. What is the real distance?

Set up: 1/25 = 4/x

Cross multiply: x = 4 × 25 = 100 km

A model car is built at a 1:24 scale. The real car is 15 feet long. How long is the model?

Scale: model/real = 1/24

Set up: 1/24 = x/15

Cross multiply: 24x = 15 → x = 15/24 = 0.625 feet (7.5 inches)

Working Backwards

Sometimes you know both the drawing measurement and the real measurement, and need to find the scale.

A room is 20 feet long. On the blueprint, it's 5 inches. What is the scale?

Scale: 5 inches = 20 feet

Simplify: 1 inch = 4 feet

Scale: 1 in : 4 ft

💡 Unit consistency: Make sure both measurements use the same units when writing the scale ratio. Convert if needed before simplifying.

🎯 Practice Problems

1. Scale: 1 in = 5 ft. A wall is 3 inches on the blueprint. How long is the real wall?

A) 5 feet

B) 8 feet

C) 15 feet

D) 25 feet

2. Scale: 1 cm = 50 km. Cities are 150 km apart. How far apart on the map?

A) 1 cm

B) 2 cm

C) 3 cm

D) 7.5 cm

3. A 1:100 model. The real building is 40 meters tall. How tall is the model?

A) 0.04 m

B) 0.4 m

C) 4 m

D) 4,000 m

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🎯 Bonus Practice

1. On a map, 2 inches = 30 miles. How many miles is 5 inches?

A) 60 miles

B) 75 miles

C) 100 miles

D) 150 miles

2. A room is 12 feet wide. On a drawing it's 3 inches. What is the scale?

A) 1 in = 2 ft

B) 1 in = 3 ft

C) 1 in = 4 ft

D) 1 in = 6 ft

3. Scale: 1:50. A hallway is 8 cm on the drawing. Real length?

A) 4 m

B) 40 m

C) 400 cm

D) 0.16 cm

4. A toy car is 6 inches long. The real car is 12 feet long. What is the scale ratio?

A) 1:2

B) 1:12

C) 1:24

D) 1:6

5. Scale: 1 cm = 10 m. You need to draw a 45 m building. How many cm on the drawing?

A) 3.5 cm

B) 4 cm

C) 4.5 cm

D) 45 cm