Ratio and rate · Usually met around P6
Enlarging and shrinking shapes
Every side times the same number; angles stay the same.
How to do it
Method
Every side times the same number; angles stay the same
4 by 2, scale factor 3 → 12 by 6
Another way
Check length : width
4 : 2 → 12 : 6 → 2 : 1
In full
To enlarge a shape by a scale factor, multiply every side by the same number; to shrink it, divide every side by the same number. Enlarging just one side, or adding the same amount to every side, changes the shape, so the result is not an enlargement. After enlarging or shrinking, the shape stays the same, every angle stays the same size, and corresponding sides are all in the same ratio: a 4 by 2 rectangle enlarged by a scale factor of 3 becomes 12 by 6, and new side : old side = 3 : 1. On squared paper, count the squares along each side first, then multiply. Or look at the ratio of length to width: 4 : 2 is 2 : 1, and any enlargement of the rectangle must be 2 : 1 too.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A rectangle is 15 cm long and 3 cm wide. It is shrunk to 13 of its size. How wide is the new rectangle, in cm?
Show the answer and working
Answer: 1 cm
Shrinking to 13 divides every side by 3: 3 ÷ 3 = 1.
Example 2
Triangle A has sides of 6 cm, 7 cm and 8 cm. Triangle B is an enlargement of A, and its shortest side is 24 cm. The scale factor is □, and B's longest side is □ cm.
Fill in each box
Show the answer and working
Answer: 4，32
Shortest side to shortest side: 24 ÷ 6 = 4; the longest side is 8 × 4 = 32.
Example 3
Rectangle A is 5 cm by 2 cm; rectangle B is 15 cm by 6 cm. B is an enlargement of A.
True or false?
Show the answer and working
Answer: True
Check that every side is multiplied by the same number: 15 ÷ 5 must equal 6 ÷ 2.
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