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Grade 8 · Pythagoras
The Theorem of Pythagoras (Grade 8)
MEMORANDUM
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  / 18

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Find the hypotenuse: sides 3 cm and 4 cm.
    (2)
    3 cm4 cm?
    c2 = 9 + 16 = 25 → 5 cm✓✓ (2)
  2. 2
    Find the hypotenuse: sides 9 cm and 12 cm.
    (2)
    9 cm 12 cm ?
    c2 = 81 + 144 = 225 → 15 cm✓✓ (2)
  3. 3
    Find the missing side: hypotenuse 10 cm, one side 6 cm.
    (2)
    6 cm?10 cm
    b2 = 100 − 36 = 64 → 8 cm✓✓ (2)
  4. 4
    Find the missing side: hypotenuse 25 cm, one side 24 cm.
    (2)
    24 cm?25 cm
    b2 = 625 − 576 = 49 → 7 cm✓✓ (2)
  5. 5
    Find the hypotenuse in surd form: sides 1 cm and 2 cm.
    (2)
    1 cm2 cm?
    c2 = 1 + 4 = 5 → 5 cm✓✓ (2)
  6. 6
    Find the hypotenuse in surd form: sides 3 cm and 5 cm.
    (2)
    3 cm5 cm?
    c2 = 9 + 25 = 34 → 34 cm✓✓ (2)
  7. 7
    Is a triangle with sides 5, 12, 13 right-angled?
    (2)
    13125
    132 = 169; 25 + 144 = 169 → Yes✓✓ (2)
  8. 8
    Is a triangle with sides 6, 7, 10 right-angled?
    (2)
    100,3°1076
    100 vs 36 + 49 = 85 → No✓✓ (2)
  9. 9
    A ladder 5 m long rests 3 m from a wall. How high up the wall does it reach?
    (2)
    3 m?5 m
    h2 = 25 − 9 = 16 → 4 m✓✓ (2)
TOTAL: 18 marks
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