An enlargement makes a shape bigger without changing its shape. The scale factor tells you how many times bigger: with a scale factor of 3, every length is multiplied by 3. It is never 'add 3'. To find the scale factor, pick a pair of matching sides and divide: new length ÷ original length. To find a missing length on the image, first find the scale factor from a pair you know, then multiply the matching original side by it. The angles stay the same; only the lengths grow.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- enlargement
- a copy made bigger by the same amount in every direction
- scale factor
- how many times bigger every length becomes
- corresponding sides
- sides in the same position on the two shapes
Worked examples
This rectangle is enlarged by a scale factor of 3. How long is the image of the side marked 4 cm?
- 1.Scale factor 3 multiplies every length by 3.
- 2.4 × 3 = 12.
= 12
A 5 cm side becomes 20 cm in an enlargement. What is the scale factor?
- 1.New ÷ original.
- 2.20 ÷ 5 = 4.
= 4
In an enlargement, a 4 cm side becomes 12 cm. How long does the matching 6 cm side become?
- 1.Scale factor: 12 ÷ 4 = 3.
- 2.6 × 3 = 18.
= 18
For parents
Method: Multiply by the scale factor; find it by dividing matching sides.
What to say: How many times bigger did that side get? Does every side get that many times bigger?
Common mistakes:
- Thinks additively: adds the scale factor, or the difference between matching sides, instead of multiplying.
- Thinks 'enlarge' always means 'double', whatever the scale factor.
- Enlarges the wrong labelled side of the shape.
- Divides the original length by the image length, giving a fraction for an enlargement.
- Finds the scale factor from the matching pair of sides and gives it as the missing length.