Scale factor — Grade 7 Accelerated, what it means and where it is taught
The number every length is multiplied by.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Dilation — A resizing from a centre point by a scale factor k.
Practise this idea
9 questions in the course bank use Scale factor, in Proportional Reasoning with Scale Drawings, Dilations & Similarity, Similarity & Proportionality. The first 8 are below; the rest are in those units.
Problem 1
A figure is enlarged by scale factor 3. A side of 5 cm becomes how long?
Worked answer
15
5 × 3 = 15 cm
Problem 2
Two similar triangles have corresponding sides 6 and 15. Find the scale factor from the smaller to the larger.
Worked answer
2.5
156 = 2.5
Problem 3
A side of length 5 becomes a side of length 15 after a dilation. Find the scale factor.
Worked answer
3
k = 155
k = 3
Problem 4
A side of length 24 becomes 18. Find the scale factor.
Worked answer
0.75
k = 1824
k = 34 = 0.75
Problem 5
△ ABC ∼ △ DEF with AB = 4, DE = 10 and BC = 6. Find EF.
Worked answer
15
k = 104 = 2.5
EF = 2.5 × 6
EF = 15
Problem 6
Two similar triangles have areas 9 cm2 and 81 cm2. Find the scale factor between them.
Worked answer
3
k2 = 819 = 9
k = 3
Problem 7
△ ABC ∼ △ DEF with AB = 4 and DE = 10. Find the scale factor.
Worked answer
2.5
k = 104 = 2.5
Problem 8
△ ABC ∼ △ DEF, AB = 4, DE = 10, BC = 6. Find EF.
Worked answer
15
k = 2.5
EF = 2.5 × 6 = 15