Pythagorean Theorem Word Problem Worksheet

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Examples, solutions, videos, and worksheets to help Grade 8 students learn how to solve word problems using the Pythagorean Theorem.

How to solve word problems using the Pythagorean Theorem?

Word problems that involve the Pythagorean Theorem generally deal with right-angled triangles, where you’re given the lengths of two sides and asked to find the third side, or asked to apply the theorem in a practical context. Here’s a step-by-step approach for solving these problems.

Steps to Solve Word Problems Using the Pythagorean Theorem:

1. Read the Problem Carefully:
   Identify what you’re being asked to find (the length of a side, distance, etc.).
   Determine which parts of the problem involve a right triangle.
   Look for keywords like “right triangle,” “diagonal,” “distance,” “height,” “base,” or “hypotenuse."
   
2. Draw a Diagram:
   If one is not provided, sketch a diagram to visualize the problem.
   Label the known lengths and variables for unknown sides.
   
3. Identify the Right Triangle and Its Parts:
   Identify which sides correspond to the legs 𝑎 and 𝑏, and which side is the hypotenuse 𝑐.
   The hypotenuse is always opposite the right angle and is the longest side.
   
4. Write the Pythagorean Theorem Formula:
   𝑎² + 𝑏² = 𝑐²
   Use this formula to relate the sides of the triangle.
   
5. Substitute Known Values:
   Plug in the values for the known sides.
   
6. Solve for the Unknown Side:
   Simplify the squares and solve for the unknown side.
   Make sure to take the positive square root, since lengths cannot be negative.
   
7. Answer the Question:
   Ensure your final answer addresses the original question (e.g., finding the total distance, height, etc.).

Have a look at this video if you need to review how to use the Pythagorean Theorem to solve word problems.

• Solving Word Problems - The Pythagorean Theorem

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Pythagorean Theorem Word Problem Worksheets.

 

More Pythagorean Theorem Word Problem Worksheets

Printable
(Answers on the second page.)
Pythagorean Theorem Word Problem Worksheet #1
Pythagorean Theorem Word Problem Worksheet #2
Pythagorean Theorem Word Problem Worksheet #3

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