Create a free account now and get 3 full lessons, completely free. Get my 3 free lessons

UK: choose your country
Practise online insteadThe answer key prints on page 2.

Pythagorean theorem word problems: diagonals of rectangles

Year 9 maths · Fieldbook Learning

Name ______________________ Date __________

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

  1. A rectangular window is 24 cm wide and 7 cm tall. How long is its diagonal, in cm?
  2. A rectangular window is 24 cm wide and 10 cm tall. How long is its diagonal, in cm?
  3. A rectangular window is 60 cm wide and 11 cm tall. How long is its diagonal, in cm?
  4. A rectangular window is 80 cm wide and 18 cm tall. How long is its diagonal, in cm?
  5. A rectangular picture frame is 15 cm wide and 36 cm tall. How long is its diagonal, in cm?
  6. A rectangular window is 180 cm wide and 33 cm tall. How long is its diagonal, in cm?
  7. A rectangular picture frame is 28 cm wide and 96 cm tall. How long is its diagonal, in cm?
  8. A rectangular picture frame is 5 cm wide and 12 cm tall. How long is its diagonal, in cm?
  9. A rectangular picture frame is 24 cm wide and 45 cm tall. How long is its diagonal, in cm?
  10. A rectangular tablet is 120 cm wide and 35 cm tall. How long is its diagonal, in cm?
  11. A rectangular picture frame is 16 cm wide and 30 cm tall. How long is its diagonal, in cm?
  12. A rectangular tablet is 10 cm wide and 24 cm tall. How long is its diagonal, in cm?
  13. A rectangular screen is 72 cm wide and 210 cm tall. How long is its diagonal, in cm?
  14. A rectangular screen is 60 cm wide and 32 cm tall. How long is its diagonal, in cm?
  15. A rectangular tablet is 24 cm wide and 18 cm tall. How long is its diagonal, in cm?
  16. A rectangular tablet is 12 cm wide and 9 cm tall. How long is its diagonal, in cm?
  17. A rectangular tablet is 480 cm wide and 88 cm tall. How long is its diagonal, in cm?
  18. A rectangular tablet is 168 cm wide and 49 cm tall. How long is its diagonal, in cm?
  19. A rectangular screen is 320 cm wide and 72 cm tall. How long is its diagonal, in cm?
  20. A rectangular tablet is 33 cm wide and 180 cm tall. How long is its diagonal, in cm?
More free practice: fieldbooklearning.com/uk/practice/year-9/pythagorean-theorem-word-problems-diagonals-of-rectangles/

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.
Download CSV

Answer key: Pythagorean theorem word problems: diagonals of rectangles

  1. 25
  2. 26
  3. 61
  4. 82
  5. 39
  6. 183
  7. 100
  8. 13
  9. 51
  10. 125
  11. 34
  12. 26
  13. 222
  14. 68
  15. 30
  16. 15
  17. 488
  18. 175
  19. 328
  20. 183