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4024/12 Oct/Nov 2025, Question 17: Similar Triangles

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Using the similar triangles ABC and PQR shown, with AB = 6 cm, AC = 7 cm, PQ = 9 cm and matching angles marked, find PR and then the area of PQR given ABC's area is 16 cm².

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Work out the length PR using the scale factor between the two similar triangles.

  1. 1Scale factor = PQ/AB = 9/6 = 1.5
  2. 2PR = 7 × 1.5 = 10.5 = 21/2 cm

Answer21/2

Part (b) · 2 marks

Given that triangle ABC has area 16 cm², work out the area of triangle PQR.

  1. 1Area scale factor = (9/6)² = 2.25
  2. 2Area PQR = 16 × 2.25 = 36 cm²

Answer36

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