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Grade 7–9Common Core (CCSS) · Math: algebra

Pythagorean Theorem Worksheets — Free with Answers

Practise a² + b² = c² with new right triangles every time: hypotenuse, missing legs and real-life word problems.

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Pythagorean theorem · 14-16 years

Name: ____________________

Worked example

  1. The goal: work out the missing side of a right-angled triangle.
  2. In a right-angled triangle: a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle).
  3. Example: a = 3, b = 4. c² = 9 + 16 = 25, so c = √25 = 5.
  4. Looking for a leg? a² = c² − b². Example: c = 13, b = 5 → a² = 169 − 25 = 144 → a = 12.
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓
Example: how to solve it
1.

Legs: a = 6 cm, b = 8 cm. Hypotenuse c =

2.

A ladder leans against a wall. The foot of the ladder is 14 m from the wall and it reaches 48 m up the wall. How long is the ladder? Answer with the correct unit.

3.

Legs: a = 9 cm, b = 3 cm. Hypotenuse c =

4.

A rectangular field is 6 m long and 8 m wide. Omar walks straight across it diagonally. How long is the walk? Answer with the correct unit.

5.

Legs: a = 3 cm, b = 4 cm. Hypotenuse c =

6.

A ladder leans against a wall. The foot of the ladder is 9 m from the wall and it reaches 9 m up the wall. How long is the ladder? Answer with the correct unit.

7.

Hypotenuse c = 10 cm, leg a = 6 cm. Leg b =

8.

A ladder leans against a wall. The foot of the ladder is 12 m from the wall and it reaches 16 m up the wall. How long is the ladder? Answer with the correct unit.

9.

Legs: a = 7 cm, b = 8 cm. Hypotenuse c =

10.

A 15 m long ramp rises to a height of 9 m. How far is it along the ground? Answer with the correct unit.

11.

Legs: a = 8 cm, b = 8 cm. Hypotenuse c =

12.

A rectangular field is 12 m long and 16 m wide. Omar walks straight across it diagonally. How long is the walk? Answer with the correct unit.

13.

Hypotenuse c = 40 cm, leg a = 24 cm. Leg b =

14.

A 20 m long ramp rises to a height of 12 m. How far is it along the ground? Answer with the correct unit.

15.

Legs: a = 8 cm, b = 15 cm. Hypotenuse c =

16.

A ladder leans against a wall. The foot of the ladder is 4 m from the wall and it reaches 9 m up the wall. How long is the ladder? Answer with the correct unit.

17.

Legs: a = 6 cm, b = 7 cm. Hypotenuse c =

18.

A ladder leans against a wall. The foot of the ladder is 12 m from the wall and it reaches 4 m up the wall. How long is the ladder? Answer with the correct unit.

19.

Legs: a = 4 cm, b = 9 cm. Hypotenuse c =

20.

A rectangular field is 6 m long and 8 m wide. Maja walks straight across it diagonally. How long is the walk? Answer with the correct unit.

Answer key

  1. 1. 10 cm
  2. 2. 50 m
  3. 3. ≈ 9.5 cm
  4. 4. 10 m
  5. 5. 5 cm
  6. 6. ≈ 12.7 m
  7. 7. 8 cm
  8. 8. 20 m
  9. 9. ≈ 10.6 cm
  10. 10. 12 m
  11. 11. ≈ 11.3 cm
  12. 12. 20 m
  13. 13. 32 cm
  14. 14. 16 m
  15. 15. 17 cm
  16. 16. ≈ 9.8 m
  17. 17. ≈ 9.2 cm
  18. 18. ≈ 12.6 m
  19. 19. ≈ 9.8 cm
  20. 20. 10 m

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Topics on this worksheet

Areas on this sheet

  • Geometry · 20

Step 1 of 5

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Your choices

Area
Geometry
Exercise type
Pythagorean theorem
Age
14–16 years
Difficulty
Easy
Number of tasks
20
Task format
Mixed
Paper size
US Letter
1. Choose content
Area
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How to use the tool

  1. Choose the exercise type Pythagorean theorem.
  2. Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
  3. Print or save as PDF. “Create new version” gives new numbers with a matching answer key.

About this generator

The Pythagorean theorem links the three sides of a right triangle. The easier level uses whole-number triples such as 3–4–5 and 5–12–13 so pupils can focus on the method. Harder levels mix in missing legs and answers rounded to one decimal. Word problems cover ladders against walls, ramps and walking diagonally across a field, and the generator also offers distance between two points in a coordinate system. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.

Popular uses

  • First lessons on right triangles
  • Ladder, ramp and diagonal problems
  • Revision before a test
  • Distance in the coordinate system

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Frequently asked questions

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
What is the Pythagorean theorem?
In a right triangle the legs a and b and the hypotenuse c satisfy a² + b² = c².
How do I find a missing leg?
Subtract: b² = c² − a², then take the square root.

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