216 CHAPTER 5 ■ SIMILAR TRIANGLES Exercises 5.1 In Exercises 1 to 4, give the ratios in simplified form. 1. a) 12 to 15 c) 1 ft to 18 in. b) 12 in. to 15 in. d) 1 ft to 18 oz 2. a) 20 to 36 c) 20 oz to 2 lb (1 lb = 16 oz) b) 24 oz to 52 oz 3. a) 15:24 b) 2 ft:2 yd (1 yd = 3 ft) d] 2 m: 1 lb 4. a) 24:32 c) 150 cm:2 m d) 1 gal:24 mi b) 12 in.:2 yd d) 2 lb to 20 oz c) 2 m: 150 cm (1 m = 100 cm) In Exercises 5 to 14, find the value of x in each proportion. 9 12 x 5. a) = 4 x1 6. a) = 10 5 7 b) = x 21 24 x-1 10 b) == 6 12 x-1 4x-1 b) = 6 18 32 b) x = = 3 2 7. a) 8 24 9 x 8. a) = x 16 x 7 9. a) b) 4 x 6 x x+1 10 x 2 12 10. a) == b) 3 x + 2 5 x + 2 x + 1 10 2x + 1 11. a) b) x 2x r1 14 3x1 x+1 12. a) = b) = 2 x 3 5 x-2 x + 1 2x 2x 13. a) b) x 3 x-1 5 x + 1 x x 2 2x 14. a) = b) = x X x x 19. An electrician installs 25 electrical outlets in a new six- mom house. Assuming proportionality, how many outlets should be installed in a new construction having seven moms? (Round to nearest integer.) 20. The secretarial pool (15 secretaries in all) on one floor of a corporate complex has access to four copy machines. If there are 23 secretaries on a different floor, approximately what number of copy machines should be available? (Assume a proportionality.) 21. Assume that AD is the geometric mean of BD and DC in AABC shown in the accompanying drawing. a) Find AD if BD = 6 and DC = 8. b) Find BD if AD = 6 and DC = 8. B D x - 3 x + 3 = 15. Sarah ran the 300-m hurdles in 47.7 sec. In meters per second, find the rate at which Sarah ran. Give the answer to the nearest tenth of a meter per second. 16. Fran has been hired to sew the dance troupe's dresses for the school musical. If 13 yd of material is needed for the four dresses, find the rate that describes the amount of material needed for each dress. In Exercises 17 to 22, use proportions to solve each problem. 17. A recipe calls for 4 cggs and 3 cups of milk. To prepare for a larger number of guests, a cook uses 14 eggs. How many cups of milk are needed? 18. If a school secretary copies 168 worksheets for a class of 28 students, how many worksheets must be prepared for a class of 32 students? Exercises 21, 22 22. In the drawing for Exercise 21, assume that AB is the geometric mean of BD and BC. 23. a) Find AB if BD = 6 and DC = 10. b) Find DC if AB = 10 and BC = 15. The salaries of a secretary, a salesperson, and a vice president for a retail sales company are in the ratio 2:3:5. If their combined annual salaries amount to $124,500, what is the annual salary of each? 24. The salaries of a school cook, custodian, and bus driver are in the ratio 2:4:3. If their combined monthly salaries for November total $8,280, what is the monthly salary for each person? 25. If the measures of the angles of a quadrilateral are in the ratio 3:4:5:6, find the measure of each angle. 26. If the measures of the angles of a quadrilateral are in the ratio of 2:3:4:6, find the measure of each angle. 27. The measures of two complementary angles are in the ratio 4:5. Find the measure of each angle, using the two methods shown in Example 7. 28. The measures of two supplementary angles are in the ratio of 2:7. Find the measure of cach angle, using the two methods of Example 7. 29. 30. If 1 in. equals 2.54 cm, use a proportion to convert 12 in. to centimeters. (HINT: 2.54 cm x cm) If 1 kg equals 2.2 lb, use a proportion to convert 12 pounds to kilograms. Unless otherwise noted, all content on this page is Cengage Learning. Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to dectron e rights, same third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 5.2 Similar Polygons 217 WX 31. For the quadrilaterals shown, MN = NP = P = 2. If MN = 7, WX = 3, and PQ = 6, find YZ 37. On a blueprint, a 1-in. scale corresponds to 3 ft. To show a room with actual dimensions 12 ft wide by 14 ft long, what dimensions should be shown on the blueprint? W Exercises 31, 32 32. For this exercise, use the drawing and extended ratio of Exercise 31. If NP 2 XY and WZ = 3½, find MQ. 38. To find the golden ratio (see the Discover activity on page 215), solve the equation ½ = 1 for L. (HINT: You will need the Quadratic Formula.) W L 33. Two numbers a and b are in the ratio 3:4. If the first number is decreased by 2 and the second is decreased by 1, they are in the ratio 2:3. Find a and b. W L-W 39. Find a) the exact length of an ideal rectangle with width W = 5 by solving = 5 34. Two numbers a and b are in the ratio 2:3. If both numbers are decreased by 2, the ratio of the resulting numbers becomes 3:5. Find a and b. 35. If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:3, find the measure of the angle. 36. If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:4, find the measure of the angle. 5.2 KEY CONCEPTS b) the approximate length of an ideal rectangle with width W = 5 by using L ≈ 1.62W. 40. Prove: If = (where a, b, c, and d are nonzero), then= 41. Prove: If (where b + 0 and d + 0), then a + b Similar Polygons Similar Polygons Congruent Polygons Corresponding Vertices, Angles, and Sides