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0580/32 May/Jun 2025, Question 22: Area of a Triangle

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 7 marks

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The question, in short

Right-angled triangle with legs 2x − 5 and 2x + 2 and hypotenuse 4x − 9; find a simplified perimeter expression, then use perimeter 40 cm to find x and the area.

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

Part (a) · 2 marks

Write the triangle's perimeter as an expression in x, fully simplified.

  1. 1Perimeter = (2x − 5) + (2x + 2) + (4x − 9)
  2. 2= 8x − 12

Answer8x − 12

Part (b) · 2 marks

Given the perimeter equals 40 cm, determine x.

  1. 1Perimeter: (2x − 5) + (2x + 2) + (4x − 9) = 40
  2. 2Collect terms: 8x − 12 = 40
  3. 38x = 52
  4. 4x = 52 ÷ 8 = 6.5

Answer6.5

Part (c) · 3 marks

Using perimeter 40 cm, calculate the triangle's area.

  1. 1From the perimeter, x = 6.5
  2. 2Shorter sides: 2 × 6.5 − 5 = 8 and 2 × 6.5 + 2 = 15
  3. 3Area = 1/2 × 8 × 15
  4. 4Area = 60 cm²

Answer60

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Also searched as: 0580/32/M/J/25 · 0580_s25_qp_32 · 0580 s25 32 · question 22.
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