Scale drawings, maps & models drills

Use a scale factor to relate drawing/map/model lengths to actual lengths.

Free, timed SHSAT practice sets on scale drawings, maps & models— every question includes a full worked explanation, and there's no account required.

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How to solve scale drawing and map problems

A scale such as "1 inch represents 40 miles" tells you how many real units one drawing unit stands for.

Common traps:

Quick check: the real distance is always much larger than the distance on the map or model.

Worked examples

Example 1.
On a blueprint, 1 inch represents 50 feet. If two landmarks are 10 inches apart on the blueprint, what is the actual distance between them?
Show answer and explanation
Answer:
C

Actual distance \(= 10 \times 50 = 500\) feet. (Dividing, \(10 \div 50\), gives 0.2. Ignoring the scale and using the drawing length gives 10. Adding, \(10 + 50\), gives 60.)

Example 2.
On a nautical chart, 1 inch represents 90 miles. Two towns are actually 180 miles apart. How far apart are they on the nautical chart, in inches?
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Answer:
A

Drawing distance \(= 180 \div 90 = 2\) inches. (Multiplying, \(180 \times 90\), gives 16200. Ignoring the scale and using the actual distance gives 180. Subtracting, \(180 - 90\), gives 90.)

Example 3.
A scale model uses a scale of 1 centimeter = 5 meters. A part measures 5 centimeters on the scale model. What is the actual length of that part, in millimeters?
Show answer and explanation
Answer:
A

Scale step: \(5 \times 5 = 25\) meters. Convert to millimeters: 1 meter = 1000 millimeters, so multiply. \(25 \times 1000 = 25000\) millimeters. (Stopping after the scale step leaves 25 meters. Dividing by 1000 instead of multiplying gives 0.025. Skipping the scale and converting the 5 centimeters directly, \(5 \times 1000\), gives 5000.)