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4 15. The Pythagorean Theorem. ALGEBRA 1 LESSON 11-2. pages 587–590 Exercises 1. 10 2. 25 3. 17 4. 26 5. 2.5 6. 1 7. 4 8. 5 9. 12 10. 7.1 11. 7.5. 24. no 25. yes 26. 1.5 27. or 0.3 28. 3 29. 6 30. 2.6 31. 7.0 32. a. 6 5 ft b. 80.5 ft 2
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4 15 The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 pages 587–590 Exercises 1. 10 2. 25 3. 17 4. 26 5. 2.5 6. 1 7. 4 8. 5 9. 12 10. 7.1 11. 7.5 24. no 25. yes 26. 1.5 27. or 0.3 28. 3 29. 6 30. 2.6 31. 7.0 32.a. 6 5 ft b. 80.5 ft2 33. yes 34. no 12. 0.6 13. 1.2 m 14. about 15.5 ft 15. about 5.8 km 16. yes 17. no 18. no 19. yes 20. no 21. yes 22. yes 23. no 11-2
The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 35. yes 36. yes 37. 4.2 cm 38. 1000 lb 39. 559.9 40. 9.0 41. 9.7 42.a. These lengths could be 2 legs or one leg and the hypotenuse. b. about 12.8 in. or 6 in. 43.a. 62 + 82 = 36 + 64 = 100 = 102 b. 5; 12; 7; 41 c. Answers may vary. Sample: 10, 24, 26 44.a. 6.9 ft b. 89.2 ft2 c. 981 watts 45. 12.8 ft 46.a. Answers may vary. Sample: 5, 20, 5 b. 5 units2 47.a. 13.4 ft b. 17.0 ft c. 10.6 ft d. No; the hypotenuse d must be longer than each leg. 48. An integer has 2 as a factor; the integer is even; if an integer is even, then it has 2 as a factor; true. 11-2
The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 54. 10 55. 4 3 56. 5 57.n2 + (n + 1)2 = (n + 2)2; 3, 4, 5 58.a. b. 74 59.a.a2 + 2ab + b2 b.c2 c. d. (a + b)2 = c2 + 4 ab ; a2 + 2ab + b2 = 2ab + c2; a2 + b2 = c2 e. This equation is the same as the Pythagorean Theorem. 49. A figure is a square; the figure is a rectangle; if a figure is a rectangle then the figure is a square; false. 50. You are in Brazil; you are south of the equator; if you are south of the equator you are in Brazil; false. 51. An angle is a right angle; its measure is 90°; if the measure of an angle is 90°, then it is a right angle; true. 52. 52 units2 53. 6 in. ab 2 1 2 11-2
– – – – > > 2 6v v4 2 2x2 6 3 The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 69. 2b2 10b 70. 71. 72. 3 and 4 73. 8 and 9 74. –8 and –7 75. 11 and 12 76. rational 77. irrational 78. irrational 79. rational 60. D 61. H 62. B 63. C 64. A 65.[2] It is a right triangle. Substitute 17, the longest side, for c and substitute the other lengths for a and b in the Pythagorean Theorem 82 + 152 172 64 + 225 289 289 = 289 [1] incorrect equation OR incorrect explanation 66. 4 3 67. 68. 5 2 11-2
The Pythagorean Theorem ALGEBRA 1 LESSON 11-2 80. 8x2 – 4x 81. 12a2 + 15a 82. 18t3 – 6t2 83. –10p4 + 26p3 84. 15b3 + 5b2 – 45b 85. –7v4 + 42v2 – 7v 11-2
