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. 22. Plato (380 BC) is credited with the following formulae that can be used to generate Pythagorean Triples. a = 2 m b = m 2 1 , c = m 2 + 1 Use the technique of Example 6 to demon- strate that the formulae given above will generate Pythagorean Triples, provided that m is a positive integer larger than 1. Secondly, generate at least 3 instances of Pythagorean Triples with Plato’s for- mula.
Section 9.6 The Pythagorean Theorem 973 Version: Fall 2007 In Exercises 23 - 28 , 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. 23. Fritz and Greta are planting a 12- foot by 18-foot rectangular garden, and are laying it out using string. They would like to know the length of a diagonal to make sure that right angles are formed. Find the length of a diagonal. Approxi- mate your answer to within 0.1 feet. 24. Angelina and Markos are planting a 20-foot by 28-foot rectangular garden, and are laying it out using string. They would like to know the length of a diag- onal to make sure that right angles are formed. Find the length of a diagonal.

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