Pre-Calculus Homework Solutions 85

# Pre-Calculus Homework Solutions 85 - 28 QRS is equilateral...

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Unformatted text preview: 28. QRS is equilateral so all three sides are congruent. QR ¬2x 2 RS ¬x 6 QS ¬3x 10 QR ¬RS 2x 2 ¬x 6 2x x ¬6 2 x ¬8 QR ¬2x 2 ¬2(8) 2 ¬14 RS ¬x 6 ¬8 6 ¬14 QS ¬3x 10 ¬3(8) 10 ¬14 29. JL ¬2x 5 JK ¬x 3 KL ¬x 1 KJ ¬LJ KJ ¬LJ x 3 ¬2x 5 3 5 ¬2x x 8 ¬x JL ¬2x 5 ¬2(8) 5 ¬11 JK ¬x 3 ¬8 3 ¬11 KL ¬x 1 ¬8 1 ¬7 30. P is the midpoint of MN, so MP PN 1 (24) or 2 12. OP MN, so MPO and NPO are right triangles. Use the Pythagorean Theorem to find MO and NO. (MO)2 ¬(MP)2 (OP)2 (MO)2 ¬122 122 (MO)2 ¬288 MO ¬ 288 (NO)2 ¬(PN)2 (OP)2 (NO)2 ¬122 122 (NO)2 ¬288 NO ¬ 288 MPO and NPO are not equilateral because MO NO 288. 31. Let x be the distance from Lexington to Nashville. Then the distance from Cairo to Nashville is x 40, the distance from Cairo to Lexington is x 81, and (x 40) (x 81) x 593 3x 41 ¬593 3x ¬552 x ¬184 x 40 ¬184 40 or 144 x 81 ¬184 81 or 265 The triangle formed is scalene; it is 184 miles from Lexington to Nashville, 265 miles from Cairo to Lexington, and 144 miles from Cairo to Nashville. ¬ (3 5)2 ( 1 4)2 ¬ 4 25 29 BC ¬ (7 3)2 [ 1 ( 1)]2 ¬ 16 0 16 or 4 AC ¬ (7 5)2 ( 1 4)2 ¬ 4 25 29 Since AB and AC have the same length, ABC is isosceles. AB ¬ [5 ( 4)]2 (6 1)2 ¬ 81 25 106 BC ¬ ( 3 5)2 ( 7 6)2 ¬ 64 169 233 AC ¬ [ 3 ( 4)]2 ( 7 1)2 ¬ 1 64 65 ABC is scalene because no two sides are congruent. AB ¬ [ 7 ( 7)]2 ( 1 9)2 ¬ 0 100 100 or 10 BC ¬ [4 ( 7)]2 [ 1 ( 1)]2 ¬ 121 0 121 or 11 AC ¬ [4 ( 7)]2 ( 1 9)2 ¬ 121 100 221 ABC is scalene because no two sides are congruent. AB ¬ [2 ( 3)]2 [1 ( 1)]2 ¬ 25 4 29 BC ¬ (2 2)2 ( 3 1)2 ¬ 0 16 16 or 4 AC ¬ [2 ( 3)]2 [ 3 ( 1)]2 ¬ 25 4 29 Since AB and AC have the same length, ABC is isosceles. AB ¬ (5 3 0)2 (2 5)2 ¬ 75 9 84 BC ¬ (0 5 3)2 ( 1 2)2 ¬ 75 9 84 AC ¬ (0 0)2 ( 1 5)2 ¬ 0 36 36 or 6 Since AB and BC have the same length, ABC is isosceles. AB ¬ [ 5 ( 9)]2 (6 3 0)2 ¬ 16 108 124 BC ¬ [ 1 ( 5)]2 (0 6 3)2 ¬ 16 108 124 AC ¬ [ 1 ( 9)]2 (0 0)2 ¬ 64 0 64 or 8 Since AB and BC have the same length, ABC is isosceles. 32. AB 33. 34. 35. 36. 37. 87 Chapter 4 ...
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