The idea, step by step
Lengths share one factor
A scale factor multiplies every matching length by the same positive number. A scale of 1:50 compares one drawing unit with fifty real units of the same kind.
Convert into a common unit before forming the ratio. The scale factor has no unit. If a small model is enlarged, the factor should be greater than one.
Use correspondence, not appearance
Identify matching sides before setting up a proportion. A diagram may be a sketch rather than a perfectly scaled picture. Its labels, not its apparent size, determine the answer.
One factor works only for similar objects. Stretching a picture in width but not height changes its shape, so similarity cannot be assumed.
A common trap
Applying a length scale as an area scale.
Instead: A drawing scale initially compares lengths. Areas use the square of that factor.
See the thinking
Room plan
A 1:50 plan shows a room length of 8 cm. Find real length in metres.
- 8×50=400 cm.
- 400 cm=4 m.
Photograph enlargement
A 12 cm wide, 8 cm high picture is enlarged to width 18 cm without distortion. Find its new height.
- k=18/12=1.5.
- Height=8×1.5=12 cm.
Check your understanding
A 1:100 plan shows a length of 3.5 cm. Find the real length.
Show answer
3.5 m
3.5×100=350 cm.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- A 1:200 plan shows a 6 cm wall. Find real length.2 marks
- A 1:25 model boat is 32 cm long. Find real length.2 marks
- Enlarge a 15 cm length by factor 1.2. Find the new length.2 marks
- A 9 m wall is drawn as 18 cm. Find the scale.2 marks
- Similar triangles have matching sides 4 and 10 cm. A 7 cm side of the smaller matches what larger length?2 marks
- A 20 by 12 cm picture is reduced to width 15 cm without distortion. Find height and justify your factor.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A 1:200 plan shows a 6 cm wall. Find real length.2 marks
6×200=1200 cm=12 m.
12 m - A 1:25 model boat is 32 cm long. Find real length.2 marks
32×25=800 cm=8 m.
8 m - Enlarge a 15 cm length by factor 1.2. Find the new length.2 marks
15×1.2=18.
18 cm - A 9 m wall is drawn as 18 cm. Find the scale.2 marks
900 cm compared with 18 cm gives 18:900=1:50.
1:50 - Similar triangles have matching sides 4 and 10 cm. A 7 cm side of the smaller matches what larger length?2 marks
k=10/4=2.5.
7×2.5=17.5.
17.5 cm - A 20 by 12 cm picture is reduced to width 15 cm without distortion. Find height and justify your factor.3 marks
k=15/20=0.75 for all corresponding lengths.
12×0.75=9.
9 cm
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Surface area of composite solids; volume of composite solids; proportion/scaling of objects; related length/area/volume factors; measurement error; the effect of rounding and repeated approximations; practical design models; evaluating assumptions and suitable precision.
Official curriculum source ↗