Chapter 11 Similarity Problems

Transcription

1 hapter Similarit roblems. ind the ratio of the perimeter of rectangle to the perimeter of rectangle L. L 4. Δ and ΔL are similar. ind the ratio of their corresponding sides. 5 ft ft 9 ft ft 0 m 8 m [] 4 [] 4 [] 5 [] 9 L 2. Solve the proportion. 8 9 = 2 p 5 m 2 m [] 0.5 [] 28.5 [] 0 [] 29. cit is developing plans for a new communit sports facilit. ommunit members can submit suggestions for the new facilit, along with basic scale drawings of their ideas. ill wants to include a new 5- b 0-meter basketball court in the athletic center. He is submitting a scale drawing on an 8.5- b -inch sheet of paper. Which scale should ill use to create as large a drawing as possible on the paper? [] 2 [] 2 [] 5 6 [] 8 5 [] [] in. = m [] 8 in. = m [] 4 in. = m 2 5 in. = m 6

2 hapter Similarit roblems 5. The shipping crates shown are similar. ind the ratio of their volumes. 8. ~ GH What is the length of? 7 cm 6 in. 7 cm 9 cm 4 cm 5 in. 2 in. [] 49 6 [] 4 64 [] 7 4 [] 2 64 H G 6. The shipping crates shown are similar. ind the ratio of their surface areas. 5 cm 5 cm 7 cm cm [] 5 [] [] 25 9 [] ~ GH What is the length of? 5 in. 8 in. 6 in. H G 2

3 hapter Similarit roblems 9. ΔR ~ ΔO ind a, b, and c if the perimeter of ΔO is 45 inches. ll measurements are in inches.. Δ ~ ΔGH ind. 4 in. 28 in in. R 57 O b c a G 0. ΔR ~ ΔO ind a, b, and c if the perimeter of ΔO is 8 inches. ll measurements are in inches. H 6 in. 2 in. 2. Δ ~ Δ G ind. 9 in. R b O c 5 a 6 G

4 hapter Similarit roblems. The pentagons and L below are similar, but not necessaril drawn to scale. ind the values of and. 4. The trapezoids and L below are similar, but not necessaril drawn to scale. ind the values of and. 8 mm 5. The trapezoids and L below are similar, but not necessaril drawn to scale. ind the values of and. 4 mm b + 2g mm 20 mm b + 2g mm b +g mm 0 mm 2 mm L 2 mm 2 mm L 2 mm 8 mm 4 mm L 5 mm 5 mm [] = 8; = [] = 8; = 4 [] = 9; = 4 [] = 9; = b + 2g mm b + g mm [] = 8; = 6 [] = 9; = 5 [] = 8; = 5 [] = 9; = 6 b + 2g mm [] = 9; = 4 [] = 9; = 5 [] = 0; = 4 [] = 0; = 5 4

5 hapter Similarit roblems 6. Given that m m and m m, find and. (Round to the nearest two decimal places when necessar.) 7 ft 4 ft 20. Given that Y, find. 8 d 4 ft ft 2 d 5 d 7. Given that m m and m m, find and. (Round to the nearest two decimal places when necessar.) 2 ft 0 ft 2. Given that Y, find. 7 d 2 ft 7 ft 2 d 4 d 8. Given that m m and m m, find and. (Round to the nearest two decimal places when necessar.) 22. re Δ and Δ similar? plain wh or wh not. 6 ft 9 ft 2 mm 6 mm 9 ft 6 ft 20 mm 5 mm 9. Given that m m and m m, find and. (Round to the nearest two decimal places when necessar.) 4 mm mm 8 ft 0 ft 0 ft 7 ft 5

6 hapter Similarit roblems 2., find the length of. 27. ind and. 6 in. 2 in. 8 in. 2 m 5 m L 9 m 7 m 28. ind and. 24., find the length of. 25 m 0 m L 8 m 0 m 0 in. 5 in. 25., find the length of. 8 in. 2 in. 2 in. 29. In Δ RST, RS = 4 centimeters, RT = 0 centimeters, and ST = 7 centimeters. In Δ UVW, UV = 28 centimeters, UW = 20 centimeters, and VW = 4 centimeters. Which statement of similarit identifies the two similar triangles and gives the correct justification of their similarit? [] ΔRST ~ ΔWUV ; SS similarit [] ΔRST ΔUVW; SSS similarit [] ΔRST ~ ΔVWU ; SSS similarit [] The triangles are not similar. 5 in. 0. Two ladders are leaning against a wall at the same angle as shown. How long is the shorter ladder? 26. ind and. 45 ft 0 ft 24 m 0 m L 7 m 0 m 2 ft 6

7 hapter Similarit roblems. The etendable ramp shown below is used to move crates of fruit to loading docks of different heights. When the horizontal distance is 2 meters, the height of the loading dock,, is 4 meters. What is the height of the loading dock,? 4. Lnn wants to find the height of the tallest building in her cit. She stands 5 feet awa from the building. There is a tree 7 feet in front of her that is 25 feet tall. How tall is the building to the nearest foot? 4 m 2 m 5 m [] 02 ft [] 925 ft [] 22 ft [] 926 ft 2. The etendable ramp shown below is used to move crates of fruit to loading docks of different heights. When the horizontal distance is 8 meters, the height of the loading dock,, is 4 meters. What is the height of the loading dock,? 5. ichelle wants to find the height of the tallest building in her cit. She stands 0 feet awa from the building. There is a tree 6 feet in front of her that is 2 feet tall. How tall is the building to the nearest foot? 4 m [] 74 ft [] 59 ft [] 756 ft [] 7 ft 8 m 2 m. mber wants to find the height of the tallest building in her cit. She stands 2 feet awa from the building. There is a tree 0 feet in front of her that is 9 feet tall. How tall is the building to the nearest foot? 6. ΔHS ~ ΔUG ind. H U 44.4 cm 4.8 cm G 7 cm S [] 570 ft [] 50 ft [] 204 ft [] 205 ft [] 4.8 cm [] 44.8 cm [] 5.92 cm [] 7.76 cm 7

8 hapter Similarit roblems 7. ind the value of that will allow ΔSI to be similar to Δ. S I 48 mm 80 mm 0 mm [] 8 mm [] 50 mm [] 4 mm [] 55 mm 8. ind the value of that will allow ΔSI to be similar to Δ. S I 50 mm 27 mm 0 mm [] 45 mm [] 4 mm [] 6 mm [] 40 mm 9. ind the value of that will allow ΔSI to be similar to Δ. S I 80 mm 45 mm 48 mm [] 57 mm [] 70 mm [] 27 mm [] 75 mm 8

9 hapter Similarit roblems 40. ind and. 20 d R T 45. storage locker shaped like a rectangular prism rents for $00 per month and is 8 feet b 5 feet b 0 feet. manda wants to give up her locker of this size and rent a new one similar in shape that has eight times the volume. ind the dimensions of her new locker. 52 d S [] = 4 2 d, = d [] = 4 d, = d 8 [] = d, = 4 d [] = d, = 4 2 d 8 4. If the sides of a square are quadrupled, how man times larger is the new area? 42. If the sides of a square are made one-seventh the original length, what fraction of the original area is the new area? [] 70 the original area [] 28 the original area [] the original area 7 [] 49 the original area 4. The rectangular shipping crates below are similar. a. ind the similarit ratio of the crate on the left to the crate on the right. b. ind the ratio of their volumes. 46. onstance is wrapping a gift to take to a part and needs a bo for the gift. The onl bo she has measures 6 inches 6 inches 6 inches. She needs a bo with measurements 2 times as large. What is the volume of the bo onstance needs? How does that volume compare to the volume of the bo she alread has? [] 728 in ; The volume of the bo onstance needs is 8 times that of the bo she has. [] 864 in ; The volume of the bo onstance needs is 8 times that of the bo she has. [] 42 in ; The volume of the bo onstance needs is 2 times that of the bo she has. [] 864 in ; The volume of the bo onstance needs is 4 times that of the bo she has. 4 ft ft 4 ft 6 ft 44. The ratio of the lengths of corresponding edges of two similar rectangular prisms is 4. What is the ratio of their volumes? 9

10 hapter Similarit roblems 47. onstance is wrapping a gift to take to a part and needs a bo for the gift. The onl bo she has measures 4 inches 7 inches 7 inches. She needs a bo with measurements 2 times as large. What is the volume of the bo onstance needs? How does that volume compare to the volume of the bo she alread has? [] 568 in ; The volume of the bo onstance needs is 8 times that of the bo she has. 49. OY ind the values of and. O 0 m 20 m 9 m 4 m [] 784 in ; The volume of the bo onstance needs is 8 times that of the bo she has. [] 686 in ; The volume of the bo onstance needs is 2 times that of the bo she has. [] = m ; = 7 m [] = 4 m ; = 9 m [] = 9 m ; = 285. m [] = 7 m ; = 285. m [] 784 in ; The volume of the bo onstance needs is 4 times that of the bo she has. 48. onstance is wrapping a gift to take to a part and needs a bo for the gift. The onl bo she has measures 5 inches 7 inches 7 inches. She needs a bo with measurements 4 times as large. What is the volume of the bo onstance needs? How does that volume compare to the volume of the bo she alread has? [] 920 in ; The volume of the bo onstance needs is 6 times that of the bo she has. [] 72 in ; The volume of the bo onstance needs is 4 times that of the bo she has. [] 5,680 in ; The volume of the bo onstance needs is 64 times that of the bo she has. [] 920 in ; The volume of the bo onstance needs is 64 times that of the bo she has. 0