Scale and similarity
Objective. Use scale factors to calculate corresponding lengths.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Scale and similarity describe shapes that have the same angles and proportional sides, linked by a single scale factor that multiplies every length. To find a missing length in a similar shape, find the scale factor by dividing a known pair of corresponding lengths, then multiply or divide other lengths by that factor. If a model is similar to a real object with a scale factor of 5, a 3 cm model length corresponds to 3 × 5 = 15 cm in reality. Always match corresponding sides carefully before dividing to find the scale factor.
Worked example
Two similar triangles have corresponding sides of 4 cm and 10 cm. If the smaller triangle has another side of 6 cm, find the corresponding side on the larger triangle using the scale factor.
- 1Find the scale factor: 10 ÷ 4 = 2.5
- 2Identify the corresponding side on the smaller triangle: 6 cm
- 3Multiply by the scale factor: 6 × 2.5
- 4The corresponding side is 15 cm
Answer: 15 cm
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Practice
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Start practisingCommon mistake. Pupils often match sides incorrectly between similar shapes, dividing unrelated lengths and getting a wrong scale factor. Always check which sides correspond by comparing angles or shape orientation first.
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