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Pythagorean theorem word problems: ladders

Year 8 maths · Fieldbook Learning

Name ______________________ Date __________

Draw the right triangle, decide which side is the hypotenuse, and use the Pythagorean theorem.

  1. A 15 m ladder leans against a wall. Its foot is 9 m from the wall. How high up the wall does it reach, in m?
  2. A 82 m ladder leans against a wall and reaches 80 m up the wall. How far is its foot from the wall, in m?
  3. A 5 m ladder leans against a wall and reaches 4 m up the wall. How far is its foot from the wall, in m?
  4. A 100 m ladder leans against a wall. Its foot is 28 m from the wall. How high up the wall does it reach, in m?
  5. A 85 m ladder leans against a wall. Its foot is 40 m from the wall. How high up the wall does it reach, in m?
  6. A 122 m ladder leans against a wall and reaches 120 m up the wall. How far is its foot from the wall, in m?
  7. A 25 m ladder leans against a wall. Its foot is 7 m from the wall. How high up the wall does it reach, in m?
  8. A 50 m ladder leans against a wall and reaches 48 m up the wall. How far is its foot from the wall, in m?
  9. A 58 m ladder leans against a wall. Its foot is 40 m from the wall. How high up the wall does it reach, in m?
  10. A 100 m ladder leans against a wall and reaches 96 m up the wall. How far is its foot from the wall, in m?
  11. A 10 m ladder leans against a wall. Its foot is 6 m from the wall. How high up the wall does it reach, in m?
  12. A 74 m ladder leans against a wall and reaches 70 m up the wall. How far is its foot from the wall, in m?
  13. A 145 m ladder leans against a wall. Its foot is 100 m from the wall. How high up the wall does it reach, in m?
  14. A 52 m ladder leans against a wall and reaches 48 m up the wall. How far is its foot from the wall, in m?
  15. A 145 m ladder leans against a wall and reaches 105 m up the wall. How far is its foot from the wall, in m?
  16. A 50 m ladder leans against a wall. Its foot is 14 m from the wall. How high up the wall does it reach, in m?
  17. A 296 m ladder leans against a wall and reaches 280 m up the wall. How far is its foot from the wall, in m?
  18. A 130 m ladder leans against a wall and reaches 120 m up the wall. How far is its foot from the wall, in m?
  19. A 150 m ladder leans against a wall and reaches 144 m up the wall. How far is its foot from the wall, in m?
  20. A 85 m ladder leans against a wall and reaches 75 m up the wall. How far is its foot from the wall, in m?
More free practice: fieldbooklearning.com/au/practice/year-8/pythagorean-theorem-word-problems-ladders/

Play it as a quiz game

20 of these questions as multiple choice, with near-miss wrong answers, ready for Kahoot or Blooket.

  1. Download the game's own question template: in Kahoot, Add question → Import spreadsheet; in Blooket, Create a set → Spreadsheet import.
  2. Click the matching button below, then click the first empty question row of the template and paste.
  3. Save the template (Kahoot needs .xlsx, Blooket .csv) and upload it.
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Answer key: Pythagorean theorem word problems: ladders

  1. 12
  2. 18
  3. 3
  4. 96
  5. 75
  6. 22
  7. 24
  8. 14
  9. 42
  10. 28
  11. 8
  12. 24
  13. 105
  14. 20
  15. 100
  16. 48
  17. 96
  18. 50
  19. 42
  20. 40