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Pre-Calculus Homework Solutions 168

Pre-Calculus Homework Solutions 168 - 6(x 6x 4 24 6x x 21...

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Unformatted text preview: 6(x 6x 4) 24 6x x 21. In order 17. EB DC, so by the Triangle Proportionality Theorem, ED AE BC AB . Substitute the known measures. 2x 3 ¬6 2 2(2x 3) ¬3(6) 4x 6 ¬18 4x ¬24 x ¬6 ED 2x 3 2(6) 3 or 9 3 HG GF 4) 60 60 3x x 22. In order to HG GF ¬ x 8 10 3 10 ¬ 2y ¬ 2y 3 16y BC FE PQ QR PQ QR y ¬ 40 y 3 ¬ 40 y 3 ¬ 8y 3 3 PT TS 3x and PT 3x x or 2x. 2 PT TS , QT is not parallel to RS. 25. In order to show QT RS, we must show that PQ QR ¬10 y 9 DE 2y 3 2(9) 3 or 15 20. In order to have GJ FK, it must be true that HG HJ GF JK . PT TS . Let RQ CD Chapter 6 x. Then SP 2x x PQ Because QR 10 1 3 or 13 3 ¬x PT TS . ¬ 65 22 22 ¬ 43 22 Let TS 24 24 9 ¬y x 10 ¬x 10 3 6 12 54.25 54.25 54.25 203 14.5 x)(x 8.5) 148.75 8.5x 26x 148.75 148.75 148.75 24. In order to show QT RS, we must show that 3 3) 8(2y 12x 12x ¬(17.5 ¬17.5x ¬ x2 ¬ x2 ¬26x ¬14x ¬14x ¬x PT TS . ¬ 30 9 9 9 ¬ 21 or 3 7 PT ¬ 18 12 12 TS ¬ 12 or 2 6 PQ PT Because QR TS , QT is not parallel to RS. y ¬ 2y 40 3 (x 3.5)(15.5 x) x2 54.25 3.5x ¬ 7 x (x 8.5 8.5) x ¬ 15.5 8.5x PQ QR PQ QR y 8 3.5 (x 3.5) x 3.5 17.5 x 23. In order to show QT RS, we must show that 8 10 3 x x2 10 3 8 HJ JK . 15.5x ¬6 x 10 3 ¬6x 20 ¬20 ¬10 8x 8x 2x x ¬18(x 5) ¬18x 90 ¬ 90 ¬ 30 ¬10 have GJ FK, it must be true that 21 19. BF CE and AC DF, so by the Triangle FE Proportionality Theorem, BC AB AF and AF CD FE DE . Substitute the known measures. x HJ JK . x4 ¬ x 15 5 18 15(x 15x 3x 18. BC ED, so by the Triangle Proportionality CD Theorem, BE AB AC . Substitute the known measures. 20 x5 16 ¬ x 3 20(x 3) ¬16(x 5) 20x 60 ¬16x 80 4x 60 ¬80 4x ¬140 x ¬35 AC x 3 35 3 or 32 CD x 5 35 5 or 40 x 6 ¬12(8) ¬96 ¬120 ¬20 to have GJ FK, it must be true that PQ QR PT TS x. Then PQ x 2. x 2 ¬ x or 1 2 ¬ 12.9 6 8.6 8. ¬ 4.3 or 1 8.6 2 PQ PT 1 Thus, QR TS 2 . Since the sides have proportional lengths, QT RS. 8 4 170 ...
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