UniGeniusGCSE Maths · Edexcel 1MA1

Worksheets · Foundation and Higher

Pythagoras in two dimensions

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Calculator · 3 marks

    A right-angled triangle has shorter sides of 7 cm and 11 cm.

    (a) Work out the length of the hypotenuse. Give your answer correct to 1 decimal place. (3)

  2. Question 2Non-calculator · 4 marks

    A rectangle has sides 9 cm and 12 cm.

    (a) Find its diagonal. (2)

    (b) Find how much shorter the diagonal is than travelling along both sides. (2)

  3. Question 3Non-calculator · 3 marks

    (a) A rectangle has perimeter 70 cm and diagonal 25 cm. Work out its area without assuming either side length. You must show your working. (3)

Answers and marks

Question 1

(a) 13.0 cm

  • M1 Writing 72+1127^2 + 11^2.
  • M1 Square-rooting their sum of squares.
  • A1 Correct answer: 13.0 cm.

Question 2

(a) 1515 cm

  • M1 The diagonal forms a right triangle with the two sides.
  • A1 Correct answer: 1515 cm

(b) 66 cm

  • P1 Subtract the diagonal from the two-side route.
  • A1 Correct answer: 66 cm

Question 3

(a) 300300 cm²

  • P1 Establishing (70/2)2−252(70/2)^{2}-25^{2} or an equivalent valid method.
  • P1 Establishing 600/2600/2 or an equivalent valid method.
  • A1 Correct answer: 300300 cm²

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Pythagoras in two dimensions

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