GCSE Maths Practice: congruence-and-similarity

Question 1 of 10

This question introduces the concept of scale factor in geometry. Understanding how shapes enlarge or reduce while maintaining proportionality is essential for GCSE-level geometry problems.

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\( \begin{array}{l}\text{A side measures 4 cm originally and 6 cm after enlargement.}\\ \text{What is the scale factor of enlargement?}\end{array} \)

Choose one option:

Always divide the new length by the original length. Remember: scale factor >1 means enlargement, <1 means reduction. Check that you are comparing corresponding sides.

Scale factor is a number which scales, or multiplies, the dimensions of a shape. When a shape is enlarged or reduced, the scale factor tells us how much larger or smaller the new shape is compared to the original. To calculate the scale factor, divide any length on the new shape by the corresponding length on the original shape. For example, if a side originally measures 4 cm and it increases to 6 cm after enlargement, the scale factor is 6 ÷ 4 = 1.5. A scale factor greater than 1 indicates enlargement, whereas a scale factor less than 1 indicates reduction. All corresponding sides of the shape change by this factor, and angles remain unchanged. Understanding scale factor is crucial not only for solving numerical problems but also for interpreting diagrams, maps, and models, where proportional reasoning is required. Additionally, scale factors are widely used in real-life applications such as architectural plans, models, and maps.