Enlargement using lengths
We can find similar shapes by multiplying the lengths of a shape by the scale factor:
New length = original length × scale factor.
Enlargement of scale factor 2
4 cm × 2 = 8 cm
2 cm × 2 = 4 cm
Enlargement of scale factor ½
4 cm × ½ = 2 cm
2 cm × ½ = 1 cm
Question
A triangle of base 3 m and height 2 m is enlarged using a scale factor 5.
What are the new dimensions of the triangle?
Base = 3 m × 5 = 15 m
Height = 2 m × 5 = 10 m
Remember that only the lengths are changing. The size of the angles always remain the same.
Given that a shape has been enlarged, we can calculate the scale factor.
We calculate the new length using the formula:
Old length × scale factor = new length
We can rearrange this formula to find:
Scale factor = new length ÷ old length
Question
Find the scale factor of these similar shapes.
We must compare the same length on both shapes.
In this case we will use:
Old length = 6 mm and new length = 15 mm
Scale factor = new ÷ old = 15 ÷ 6 = 2.5
Question
Boxes of matches are sold in three different sizes: small, medium and large.
The medium box is an enlargement of the small box using a scale factor 2.
- What are the dimensions of the medium box?
- What scale factor enlargement is the large box of the small box?
- What scale factor enlargement is the large box of the medium box?
- Scale factor 2: 3 cm × 2 = 6 cm, 1 cm × 2 = 2 cm, 4 cm × 2 = 8 cm. Medium box is 6 cm by 2 cm by 8 cm.
- Scale factor = new ÷ old: Small to large scale factor = 14 cm ÷ 4 cm = 3.5
- Scale factor = new ÷ old: Medium to large scale factor = 14 ÷ 8 = 1.7
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