A free printable worksheet that pairs with the Pythagorean Platforms game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

The Pythagorean Theorem

Grade 8 · CCSS 8.G.B.6, 8.G.B.7 · Pairs with the Pythagorean Platforms game

Name

Date

In a right triangle, a² + b² = c². Legs a and b make the right angle. The hypotenuse c is across from it, and it's always the longest side.
Steps: plug in → square → add (or subtract) → take the square root.

Part A: Find the hypotenuse (the rope)

1. a = 6 ft, b = 8 ft. Find c.

c = ft

2. a = 5 ft, b = 12 ft. Find c.

c = ft

3. a = 12 ft, b = 9 ft. Find c.

c = ft

4. a = 15 ft, b = 8 ft. Find c.

c = ft

Part B: Find the missing leg (the distance to the next platform)

5. c = 10 ft, b = 6 ft. Find a.

a = ft

6. c = 13 ft, b = 5 ft. Find a.

a = ft

7. c = 17 ft, a = 15 ft. Find b.

b = ft

8. c = 25 ft, a = 24 ft. Find b.

b = ft

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625

Part C: Word problems

9. An explorer's vine is tied to a branch 12 ft above her platform. The next platform is 16 ft straight across. How long must the vine be to reach it? Draw the triangle.

Answer: ft

10. A 15 ft rope hangs from an anchor 9 ft above a platform. How far across can the explorer swing to the next platform?

Answer: ft

11. A 13 ft ladder leans against a wall. Its base is 5 ft from the wall. How high up the wall does it reach?

Answer: ft

12. Find the mistake. Jordan found the hypotenuse of a triangle with legs 6 and 8 like this: c = 6 + 8 = 14. What did Jordan do wrong? Find the correct answer.

Correct c =

Answer Key: The Pythagorean Theorem

For the teacher

6² + 8² = 36 + 64 = 100, √100 → c = 10 ft
5² + 12² = 25 + 144 = 169, √169 → c = 13 ft
12² + 9² = 144 + 81 = 225, √225 → c = 15 ft
15² + 8² = 225 + 64 = 289, √289 → c = 17 ft
a² + 6² = 10², a² = 100 − 36 = 64 → a = 8 ft
a² + 5² = 13², a² = 169 − 25 = 144 → a = 12 ft
15² + b² = 17², b² = 289 − 225 = 64 → b = 8 ft
24² + b² = 25², b² = 625 − 576 = 49 → b = 7 ft
Legs 12 and 16: 144 + 256 = 400, √400 → 20 ft
Hypotenuse 15, leg 9: 225 − 81 = 144, √144 → 12 ft
Hypotenuse 13, leg 5: 169 − 25 = 144, √144 → 12 ft
Jordan added the side lengths instead of their squares. Correct: 6² + 8² = 100, √100 → c = 10. (14 can't be right: the hypotenuse has to be shorter than the two legs added together.)

Common mistakes to watch for: adding the sides (#12), doubling instead of squaring (6² = 12), stopping at c² without taking the square root, and adding instead of subtracting when finding a leg (Part B). The game's wrong answer choices are built from these same mistakes.