Similar Lengths (Cambridge (CIE) IGCSE Maths): Revision Note

Similar lengths

How do I find the scale factor between lengths on similar shapes?

• Equivalent lengths on two similar shapes will be in the same ratio and are linked by a scale factor

• Establish the type of enlargement

  • If the second shape is bigger

    • then the scale factor is greater than 1

  • If the second shape is smaller

    • then the scale factor is greater than 0 but less than 1

• To find the scale factor

  • Identify known lengths of corresponding sides

  • Divide the length on the second shape by the corresponding length on the first shape

How do I find missing lengths on similar shapes?

Method 1

• STEP 1
  Find the scale factor to get from the first shape to the second shape

  • Divide a length on the second by the corresponding length on the first

  • The scale factor can be less than 1 for this method

• STEP 2
  Use the scale factor to find the length you need

  • To find a missing length on the second shape

    • Multiply the corresponding length on the first shape by the scale factor

  • To find a missing length on the first shape

    • Divide the corresponding length on the first shape by the scale factor

Method 2

• STEP 1
  Find the scale factor to get from the smaller shape to the bigger shape

  • Divide a length on the bigger shape by the corresponding length on the smaller shape

  • The scale factor is always greater than 1 for this method

• STEP 2
  Use the scale factor to find the length you need

  • To find a missing length on the bigger shape

    • Multiply the corresponding length on the smaller shape by the scale factor

  • To find a missing length on the smaller shape

    • Divide the corresponding length on the bigger shape by the scale factor