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Pre-Calculus Homework Solutions 194

Pre-Calculus Homework Solutions 194 - 19 y RS R(0 6 S(6 6 6...

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19. QR (0 3) 2 (6 2) 2 ( 3) 2 4 2 25 or 5 RS (6 0) 2 (6 6) 2 6 2 0 2 36 or 6 QS (6 3) 2 (6 2) 2 3 2 4 2 25 or 5 QR 2 QS 2 ¬ RS 2 5 2 5 2 ¬ 6 2 25 25 ¬ 36 50 ¬ 36 Since the sum of the squares of two sides is not equal to the square of the longest side, QRS is not a right triangle. 20. QR [2 ( 4)] 2 (11 6) 2 6 2 5 2 or 61 RS (4 2) 2 ( 1 11) 2 2 2 ( 12) 2 or 148 QS [4 ( 4)] 2 ( 1 6) 2 8 2 ( 7) 2 or 113 QR 2 QS 2 ¬ RS 2 61 2 113 2 ¬ 148 2 61 113 ¬ 148 174 ¬ 148 Since the sum of the squares of two sides is not equal to the square of the longest side, QRS is not a right triangle. 21. QR [ 4 ( 9)] 2 [ 4 ( 2)] 2 5 2 ( 2) 2 or 29 RS [ 6 ( 4)] 2 [ 9 ( 4)] 2 ( 2) 2 ( 5) 2 or 29 QS [ 6 ( 9)] 2 [ 9 ( 2)] 2 3 2 ( 7) 2 or 58 QR 2 RS 2 ¬ QS 2 ( 29 ) 2 ( 29 ) 2 ¬ ( 58 ) 2 29 29 ¬ 58 58 ¬ 58 Since the sum of the squares of two sides equals the square of the longest side, QRS is a right triangle. 22. Since the measure of the longest side is 17, 17 must be c , and a or b are 8 and 15. a 2 b 2 ¬ c 2 8 2 15 2 ¬ 17 2 64 225 ¬ 289 289 ¬ 289 These segments form the sides of a right triangle since they satisfy the Pythagorean Theorem. The measures are whole numbers and form a Pythagorean triple. 23. Since the measure of the longest side is 25, 25 must be c , and a or b are 7 and 24. a 2 b 2 ¬ c 2 7 2 24 2 ¬ 25 2 49 576 ¬ 625 625 ¬ 625 These segments form the sides of a right triangle
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