GCSE Maths Practice: congruence-and-similarity

Question 2 of 10

This question introduces scale factor for enlargements. You need to calculate how much larger a shape becomes when its sides increase.

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\( \begin{array}{l}\text{A side of a shape increases from 4 cm to 12 cm.}\\ \text{What is the scale factor of enlargement?}\end{array} \)

Choose one option:

Divide new length by original length. Scale factor >1: enlargement, <1: reduction.

Scale factor tells us how dimensions change during enlargement or reduction. To calculate it, divide any side length of the new shape by the corresponding side length of the original shape. In this example, the original side is 4 cm and the enlarged side is 12 cm, so the scale factor is 12 ÷ 4 = 3. All sides are multiplied by the same scale factor, while angles remain the same. Understanding scale factor helps in solving geometry problems, interpreting maps, creating models, and working with diagrams in real life. Always check which side corresponds to which to avoid mistakes. For reductions, the scale factor will be less than 1. Mastery of this concept is key for GCSE geometry, particularly for congruence and similarity questions.