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Pythagorean Theorem Word Problems - Worksheet 10 - 8th Grade

Hard

Use a² + b² = c² for right triangles, coordinate distances and contextual problems.

hard: Solve for a missing measure or explain a relationship.

18 problems · 20-25 minutes · Skills: pythagorean theorem, problem solving, geometry

About This Worksheet

This hard-level worksheet contains 18 problems designed for 8th Grade students practicing pythagorean theorem word problems. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Read labeled dimensions and coordinates. Recall multiplication facts and length units.

  • Use a² + b² = c² for right triangles, coordinate distances and contextual problems.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: A path goes 9 m east and 12 m north. What is the straight-line distance from start to finish?
Solution Steps:
  1. Add the squares of the two perpendicular lengths.
  2. Take the positive square root.
Answer: 15 m
Tip: Check your result using the method in the example before moving to the next question.
1
A path goes 12 m east and 16 m north. What is the straight-line distance from start to finish?
2
A path goes 9 m east and 12 m north. What is the straight-line distance from start to finish?
3
A path goes 30 m east and 40 m north. What is the straight-line distance from start to finish?
4
A path goes 3 m east and 4 m north. What is the straight-line distance from start to finish?
5
A path goes 6 m east and 8 m north. What is the straight-line distance from start to finish?
6
A path goes 39 m east and 52 m north. What is the straight-line distance from start to finish?
7
A path goes 27 m east and 36 m north. What is the straight-line distance from start to finish?
8
A path goes 18 m east and 24 m north. What is the straight-line distance from start to finish?
9
A path goes 21 m east and 28 m north. What is the straight-line distance from start to finish?
10
A path goes 15 m east and 20 m north. What is the straight-line distance from start to finish?
11
A path goes 24 m east and 32 m north. What is the straight-line distance from start to finish?
12
A path goes 45 m east and 60 m north. What is the straight-line distance from start to finish?
13
A path goes 33 m east and 44 m north. What is the straight-line distance from start to finish?
14
A path goes 36 m east and 48 m north. What is the straight-line distance from start to finish?
15
A path goes 42 m east and 56 m north. What is the straight-line distance from start to finish?
16
A path goes 39 m east and 52 m north. What is the straight-line distance from start to finish?
17
A path goes 33 m east and 44 m north. What is the straight-line distance from start to finish?
18
A path goes 6 m east and 8 m north. What is the straight-line distance from start to finish?

Answer Key

1. 20 m2. 15 m3. 50 m4. 5 m5. 10 m6. 65 m7. 45 m8. 30 m9. 35 m10. 25 m11. 40 m12. 75 m13. 55 m14. 60 m15. 70 m16. 65 m17. 55 m18. 10 m

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What skills does this pythagorean theorem worksheet cover?

This worksheet focuses on pythagorean theorem, problem solving, geometry. It is designed for 8th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.