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Pythagorean theorem word problems: ladders

Grade 8 math · 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/practice/grade-8/pythagorean-theorem-word-problems-ladders/

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

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  2. Click the matching button below, then click the first empty question row of the template and paste.
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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