Finding the Hypotenuse of a 3-4-5 Right Triangle
Use the Pythagorean Theorem and the geometry problem-solving strategy to find the length of the hypotenuse of a right triangle whose legs measure and .
- Read: A right triangle has legs of length and ; find the hypotenuse.
- Identify: The length of the hypotenuse.
- Name: Let = the length of the hypotenuse. Label the figure accordingly.
- Translate: Write the Pythagorean Theorem and substitute the known leg lengths:
- Solve: Evaluate the squares: . Simplify: . Apply the square root definition: , so .
- Check: Verify by substituting back: and , so checkmark
- Answer: The length of the hypotenuse is .
This example demonstrates the basic application of the Pythagorean Theorem: substitute the two known leg lengths into , compute each square, add, and then take the square root of both sides to find the hypotenuse.
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