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4024/11 Oct/Nov 2022, Question 15: Similar Triangles

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Two similar triangles ABC and DEC share a vertex C with ACD and BCE straight; given AB = 12 cm, BC = 27 cm, CD = 7 cm, DE = 3 cm, find AC and then the area of DEC using ABC's area of 160 cm².

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Part (a) · 2 marks

Use the similarity correspondence to work out the length AC in cm.

  1. 1AC/DC = AB/DE → AC/7 = 12/3
  2. 2AC = 7 × 4 = 28 cm

Answer28

Part (b) · 2 marks

Using the area of ABC as 160 cm², work out the area of triangle DEC in cm².

  1. 1Length scale factor DEC : ABC = 3/12 = 1/4
  2. 2Area scale factor = (1/4)² = 1/16
  3. 3Area DEC = 160 ÷ 16 = 10 cm²

Answer10

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Also searched as: 4024/11/O/N/22 · 4024_w22_qp_11 · 4024 w22 11 · question 15.
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