Chap9 Section6

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 9.6 The Pythagorean Theorem 971 Version: Fall 2007 9.6 Exercises In Exercises 1 - 8 , state whether or not the given triple is a Pythagorean Triple. Give a reason for your answer. 1. (8 , 15 , 17) 2. (7 , 24 , 25) 3. (8 , 9 , 17) 4. (4 , 9 , 13) 5. (12 , 35 , 37) 6. (12 , 17 , 29) 7. (11 , 17 , 28) 8. (11 , 60 , 61) In Exercises 9 - 16 , set up an equation to model the problem constraints and solve. Use your answer to find the missing side of the given right triangle. Include a sketch with your solution and check your result. 9. 2 3 2 Copyrighted material. See: 1 10. 2 2 11. 4 8 12. 10 12 13. 2 2 3
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972 Chapter 9 Radical Functions Version: Fall 2007 14. 12 4 3 15. 5 10 16. 8 2 8 In Exercises 17 - 20 , set up an equation that models the problem constraints. Solve the equation and use the result to answer the question. Look back and check your result. 17. The legs of a right triangle are con- secutive positive integers. The hypotenuse has length 5. What are the lengths of the legs? 18. The legs of a right triangle are con- secutive even integers. The hypotenuse has length 10. What are the lengths of the legs? 19. One leg of a right triangle is 1 cen- timeter less than twice the length of the first leg. If the length of the hypotenuse is 17 centimeters, find the lengths of the legs. 20. One leg of a right triangle is 3 feet longer than 3 times the length of the first leg. The length of the hypotenuse is 25 feet. Find the lengths of the legs. 21. Pythagoras is credited with the fol- lowing formulae that can be used to gen- erate Pythagorean Triples. a = m b = m 2 1 2 , c = m 2 + 1 2 Use the technique of Example 6 to demon- strate that the formulae given above will generate Pythagorean Triples, provided that m is an odd positive integer larger than one. Secondly, generate at least 3 instances of Pythagorean Triples with Pythagoras’s formula.
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