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4MA1/2HR Jun 2024, Question 12: Similar Triangles

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks

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The question, in short

Using a diagram with parallel lines BE and CD on two straight lines from A, find ED given AE = 10 cm and CD = 1.5 × BE, then find x from AB = (2x + 5) cm and BC = (3x − 5) cm.

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

Part (a) · 2 marks

Calculate the length of ED using the parallel lines and the given lengths.

  1. 1BE is parallel to CD, so triangles ABE and ACD are similar
  2. 2CD = 1.5 × BE, so AD = 1.5 × AE = 1.5 × 10 = 15
  3. 3ED = AD − AE = 15 − 10 = 5

Answer5

Part (b) · 2 marks

Determine the value of x from the two expressions for the segments of AC.

  1. 1AB + BC = AC = (2x + 5) + (3x − 5) = 5x
  2. 2AC = 1.5 × AB → 5x = 1.5(2x + 5)
  3. 35x = 3x + 7.5
  4. 42x = 7.5
  5. 5x = 3.75

Answer3.75

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