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GCSE Maths · Ratio & proportion
Scale drawings GCSE Questions and Worked Answers
A scale drawing keeps lengths proportional. A scale 1:n means one drawing unit represents n of the same real units. Multiply a drawing length to find the real length; divide a real length to find its drawing length, keeping units consistent.
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Start with the meaning
What you need to know about scale drawings
A map can show a long road on a small page. If each 1 cm of map represents 4 m of real distance, a 3 cm line represents 12 m. The map and the real object have corresponding lengths linked by one multiplier. That relationship is the scale.
See the idea first
One map unit always represents the same real distance
A scale can carry units, such as 1 cm : 4 m. To write it as the plain ratio 1 : n, first use the same units: 4 m = 400 cm, so this is 1 : 400. That means 1 drawing centimetre represents 400 real centimetres. A plain ratio does not secretly switch from centimetres to metres.
| Drawing length | Real length | Calculation |
|---|---|---|
| 1 cm | 4 m | 1 × 4 |
| 3 cm | 12 m | 3 × 4 |
| 5.5 cm | 22 m | 5.5 × 4 |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Find a real distance
What the problem asks: At 1 cm : 3 km, what real distance does 4.5 cm represent?
How to solve it: Multiply 4.5 by 3 to get 13.5 km. The scale already states the different units explicitly.
Find a drawing length
What the problem asks: A real wall is 8 m long. Draw it at scale 1 : 200.
How to solve it: Convert 8 m to 800 cm, then divide by 200. Its drawing length is 4 cm.
Find the scale
What the problem asks: A 6 cm drawing line represents a 15 m wall. Write the scale as 1 : n.
How to solve it: 15 m = 1500 cm. The ratio 6 : 1500 simplifies by dividing both sides by 6 to 1 : 250.
A reliable routine
Convert between a drawing and reality
Use this for a proportional scale drawing or map. Matching lengths share the same ratio, so you can multiply or divide by the real distance represented by one drawing unit.
- Write what one drawing unit represents, including units.
- Convert units first if using a plain ratio 1:n.
- For scale 1 : n in matching units, multiply the drawing length by n to find the real length; divide the real length by n to find the drawing length.
- Check that the real object is larger for a reducing scale; square the factor only for areas.
Check: Do not measure a responsive webpage diagram with a ruler: screen size and zoom change it. These questions provide drawing measurements or ask you to construct a measured drawing on paper.
Fully worked
Scale drawings GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Map distance
Question
A map uses 1 cm : 2.5 km. A route measures 6 cm on the map. Find its real length.
Each map centimetre contributes 2.5 km.
Example 2
Ratio scale
Question
A plan has scale 1 : 500. A wall measures 3.4 cm on the plan. Find its actual length in metres.
A plain ratio gives the real length in the drawing's unit, centimetres, so convert to metres at the end.
Example 3
Drawing length
Question
A room is 7.2 m long. Find its plan length in cm at scale 1 : 120.
Divide because the drawing is smaller than the room.
Example 4
Find the scale
Question
A 4 cm model length represents 10 m. Give the scale as 1 : n.
Divide both ratio terms by 4.
Example 5
A complete room plan
Question
A room is 6 m by 4.5 m. At scale 1 : 150, state the dimensions of the rectangle to draw in centimetres.
Convert the real dimensions: 600 cm and 450 cm.
Draw a 4 cm by 3 cm rectangle with right angles; apply the same scale to both dimensions.
Example 6
Area scale
Question
At scale 1 : 100, a rectangular plan area is 12 cm². Find the real area in m².
Each length grows by 100, so area grows by 100².
Equivalently 1 drawing cm represents 1 real m, so 1 drawing cm² represents 1 real m².
10 original questions · total 29 marks
Scale drawings GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 34 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Simple map scale
At 1 cm : 5 km, find the real distance represented by 2.4 cm.
Show worked answer
Real distance
A drawing at 1 : 200 shows a line 8 cm long. Find its real length in metres.
Show worked answer
Model length
A real length is 9 m. Find its drawing length at 1 : 300 in cm.
Show worked answer
Map length
At 1 cm : 4 km, how long should a 30 km route be on the map?
Show worked answer
Write 1:n
A 5 cm line represents 20 m. Find the scale as 1 : n.
Show worked answer
20 m = 2000 cm.
Different drawing units
At scale 1 : 50,000, a line is 36 mm long. Find the real length in km.
Show worked answer
Two dimensions
A garden is 12 m by 8 m. Give its plan dimensions in cm at 1 : 400.
Show worked answer
Draw a 3 cm by 2 cm rectangle.
Perimeter
At scale 1 : 250, a plan rectangle is 4 cm by 2 cm. Find the real perimeter in metres.
Show worked answer
Real sides are 1000 cm = 10 m and 500 cm = 5 m.
Area
At scale 1 : 200, a plan area is 6 cm². Find the real area in m².
Show worked answer
Same line, different scale
A route is 5 cm on a 1 : 20,000 map. How long is it on a 1 : 50,000 map?
Show worked answer
Real length = 5 × 20,000 = 100,000 cm. On the second map:
The larger second number in the scale 1 : n produces the smaller drawing.
Examiner-style feedback
Common scale drawings mistakes
Convert both lengths to the same unit before simplifying to 1:n.
For a reducing scale, finding the drawing length requires division.
Area changes in two dimensions, so square the length factor.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Read one-unit correspondence.
- Use equal units in plain ratios.
- Choose multiply or divide from the direction.
- Area uses the square factor.
Quick answers
Scale drawings FAQ
Is 1:100 a larger drawing than 1:500?
For the same object, yes. Each real length is divided by 100 rather than by 500.
Can I use metres on both sides of a ratio?
Yes. A plain ratio works in any common unit; both sides must use the same one.
Content standards
Curriculum and rights review
R2/G15 scale diagrams and maps across tiers, with G19 area factors as a connected extension. On-screen artwork must not be physically measured unless a calibrated scale is provided. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references