GCSE Maths Practice: congruence-and-similarity

Question 4 of 10

This question requires applying a scale factor to find a corresponding side in similar triangles.

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\( \begin{array}{l}\text{In two similar triangles, one side measures } 5 \text{ cm and corresponds to } 10 \text{ cm.}\\ \text{Another side measures } 7.5 \text{ cm.}\\ \text{Find the corresponding side in the larger triangle.}\end{array} \)

Choose one option:

Identify scale factor from one pair of sides, then multiply other sides accordingly.

When two triangles are similar, all corresponding sides are proportional. If one side measures 5 cm and corresponds to 10 cm, the scale factor = 10 ÷ 5 = 2. To find another side, multiply by the same scale factor: 7.5 × 2 = 15 cm. Understanding how to use scale factors in similar triangles is vital in GCSE geometry. Always check which sides correspond and ensure the factor is applied consistently. Practicing these problems builds confidence in proportional reasoning and geometric proofs.