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8.G.7 [565786]StudentClassDate

1. A spear of 5.4 ft is inserted in a wooden box as shown.

What is the approximate width of the base?

A. 7 ft

B. 5 ft

C. 3 ft

D. 2 ft

2. A staircase runs along the outside of a building to the second floor.

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Which distance, to the nearest tenth of a foot, is closest to the length of the staircase?

A. 6.0 feet

B. 8.6 feet

C. 10.4 feet

D. 12.8 feet

3. The shortest side of a right triangle is 7.2 centimeters long and the longest side is 15.5 centimeters long. What is the length, to the nearest tenth of a centimeter, of the third side?

A. 8.3 cm

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B. 11.4 cm

C. 13.7 cm

D. 17.1 cm

4. In the figure below is △MNP.

What is the area of △MNP?

A. 84 cm2

B. 105 cm2

C. 158 cm2

D. 168 cm2

5. Linda bought a rectangular-shaped table.

The top of the table has a width of 56 inches.

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The diagonal of the top of the table was 64 inches.

What is the approximate area of the top of the table?

A. 1,736 square inches

B. 1,984 square inches

C. 3,584 square inches

D. 4,762 square inches

6. Bon Voyage!

Airlines have regulations about the weight and dimensions of luggage taken on board, both for carry-on and checked baggage. Some airlines provide restrictions by giving the maximum allowable sum of the dimensions of a bag—the length plus the width plus the depth (or height).

Part A. Ari wants to put a tube containing a poster in his carry-on suitcase. His carry-on suitcase has a base that is rectangular in shape and is 21 inches long by 15 inches wide. What is the maximum length of a tube that he can put on the bottom of his suitcase? Show your work. For your initial calculations, ignore the width of the tube. Give your answer to the nearest inch.

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Part B. The diameter of the tube is 3 inches. Therefore, it cannot fit all the way into the corner of his suitcase. In addition, the inside dimensions of

the suitcase are slightly smaller than the outside dimensions.

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For estimation purposes, assume that the distance from the end of the tube to the corner of the suitcase forms an altitude that creates two congruent isosceles right triangles. Using this information and your knowledge about triangles, calculate the number of inches that need to be subtracted from the maximum length in part A in order to account for the diameter of the tube. Then, give an estimate for the length of a tube with a 3-inch diameter that would actually fit in the bottom of the suitcase, to the nearest inch. Explain how you found your answer.Part C. The airline on which Ari is flying allows a maximum sum of 45 inches for the dimensions of a carry-on bag—length plus width plus depth (or height). Ari’s suitcase has the maximum possible dimensions. He would like to put a 24-inch poster tube with a 3-inch diameter in his carry-on suitcase.Think about some more ways Ari can fit his poster into the suitcase and explain whether or not he will be able to fit his poster. Use calculations if necessary, being sure to make adjustments for the width of the tube. Label the diagram below with all dimensions you know and any you may have calculated. Explain your answers and show your work.

Part D. The allowable sum of dimensions of checked bags is 62 inches on this airline. Design three sizes of bags with this allowable sum of dimensions.

Label the dimension that gives the maximum distance inside the suitcase, based on what you determined in part C.

Fill in the table to show the length, width, height, volume, and maximum distance (to the nearest inch).

In the last row, generalize how to determine the volume and maximum distance inside a suitcase using variable form.

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Part E. Compare the values for the different suitcases you calculated in your table. Which of the suitcases do you think would be most practical? Explain your answer and justify your response with examples from the numbers in your table.

7. A right triangle is shown below.

What is the approximate measure of the missing side, x?

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A. 8 cm

B. 14 cm

C. 19 cm

8. Pythagoras and TVsYour family is considering buying a certain entertainment center with shelves of various sizes for a TV, books, pictures, knickknacks, and other items. You are thinking about how you might place different items on the shelves.

The largest opening in the entertainment center is for a TV. It is 46 inches wide and 33 inches high. The size of a TV screen is given as the diagonal length, and you want to find out the maximum diagonal size of a TV that will fit in that space, leaving at least 3 inches on each side and 3 inches at the top. There will also be a stand that is about 3 inches high.

Part A. Given the dimensions of the entertainment center and the restrictions on space, including the space that needs to be left on each side, the top, and for the TV stand, what are the maximum dimensions of a TV that would fit into this entertainment center? Make sure to include the maximum width, height, and diagonal. Round your answers to the nearest inch, if necessary.

Part B. The dimensions of the TV screen will be in the ratio 16:9. In other

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words, for every 16 inches of width the screen will be 9 inches high. Knowing this, what are the dimensions of the largest TV that will fit into the entertainment center? Make sure to include the width, height, and diagonal. Show your work using pictures, words, and/or equations.

Part C. You also have a hand-carved spear from South America. It is 34 inches long. One of the compartments in the entertainment center is 30 inches wide and 15 inches deep. The spear is too long to fit in the compartment straight across. Could it fit diagonally across the bottom of the compartment? Show your work.

Part D. Would it be possible to fit the spear in the compartment with one end at the upper left front corner and the other end in the lower back right corner if the shelf is 15 inches high? (See the diagram below.) Explain your answer and show your calculations.

9. There is a pole located in a garden. The pole’s base is 4.5 feet west and 5.1 feet north of a brick that marks the entrance of the garden. A bird is sitting on top of the pole. If the pole is 6 feet tall, approximately how far is the bird from the brick that marks the entrance of the garden?

A. 6.8 feet

B. 7.5 feet

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C. 7.9 feet

D. 9.1 feet

10. Which measurements below are lengths of the sides of a right triangle?

A. 10 cm, 24 cm, 39 cm

B. 15 cm, 24 cm, 28 cm

C. 20 cm, 48 cm, 52 cm

D. 25 cm, 50 cm, 75 cm

11. The diagonal of the face of a cube is 6 centimeters (cm).

What is the height, h, of the cube?

A. cm

B. 3 cm

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C. cm

D. 6 cm

12. What is the length of the hypotenuse in the right triangle below?

A. 8 in.

B. 15 in.

C. 20 in.

D. 21 in.

13. On an adult baseball field, the distance from each base to the center of the field is approximately 64 feet.

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On a children’s baseball field, the distance from each base to the center of the field is approximately 21 feet shorter than the corresponding distance on the adult baseball field. Which approximation is closest to the distance between the bases on a children’s baseball field?

A. 43 feet

B. 61 feet

C. 70 feet

D. 86 feet

14. What is the perimeter of △JKL below?

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A. 28 cm

B. 30 cm

C. 34 cm

D. 36 cm

15. The size of a rectangular television screen is described by the length of its diagonal, rounded to the nearest whole number. If the height of a television is 18 inches and the width is 32 inches, what is the length of the television's diagonal, to the nearest inch?

A. 14

B. 25

C. 37

D. 50

16. Sara draws a rectangle with a length of 78 inches and a width of

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39 inches. She draws a diagonal line from one corner to the other. Approximately how long is the diagonal line?

A. 59 inches

B. 68 inches

C. 87 inches

D. 117 inches

17. Emily made a felt craft pattern by drawing right triangles of different side lengths. She drew triangles such that the length of the longest side was a centimeters and the length of the shortest side was centimeters.

Part A. Use the Pythagorean theorem to calculate the approximate length of the third side, if the length of the shortest side of Emily’s triangle was 9 centimeters long.

Part B. What was the length of each of the sides of Emily’s triangle if centimeters?

Use words, numbers, and/or pictures to show your work.


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What is the measure of the missing side, x?

A. 4 cm

B. 8 cm

C. 12 cm

19. A square checkerboard has four sides that are each 15 inches long. About how far will a checker travel if it starts in one corner of the board and travels diagonally to the opposite corner of the board?

A. 30 inches

B. 25 inches

C. 20 inches

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D. 15 inches

20. The side lengths of a square are 16 cm each. What is the approximate length of the diagonal of the square?

A. 17 cm

B. 23 cm

C. 24 cm

D. 32 cm

21. In triangle WXY below, XY measures 16 cm, YZ measures 4 cm, and WX measures 13 cm.

What is the area of triangle WXY?

A. 40 cm2

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B. 60 cm2

C. 80 cm2

D. 100 cm2

22. A rope 10 feet long is tied to the top of an 8-foot pole.

If the rope is pulled tightly, how far from the bottom of the pole should the rope be staked to the ground?

A. 2 feet

B. 6 feet

C. 9 feet

D. 13 feet

23. The legs of a right triangle measure 4 inches and 7 inches. What is the approximate length of the hypotenuse?

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A. 8 inches

B. 10 inches

C. 11 inches

D. 14 inches

24. Carmen leaned a 13-foot ladder against a wall. If the base of the ladder is 4 feet from the bottom of the wall, approximately how far up the wall does the ladder reach?

A. 9.0 feet

B. 12.4 feet

C. 13.6 feet

D. 17.0 feet


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What is the measure of the missing side, x?

A. 13 cm

B. 12 cm

C. 8 cm

26. In the picture below, an airplane is 40 miles (air distance) from the airport and is at an elevation of 4 miles.

What is the approximate ground distance (d) the airplane is from the airport?

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A. 20.4 mi

B. 36.0 mi

C. 39.8 mi

D. 44.0 mi

27. A 20-foot (ft) ladder is leaning against a building, as shown.

At what height, x, does the ladder touch the wall?

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A.

B.

C.

D.

28. Which set of measurements could be the side lengths of a right triangle?

A. {10 cm, 12 cm, 16 cm}

B. {20 cm, 21 cm, 29 cm}

C. {30 cm, 32 cm, 42 cm}

D. {40 cm, 42 cm, 56 cm}

29. A hot air balloon is tied to the ground by a 200-yd rope as shown in the picture below.

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The balloon is floating 20 yds west of where the rope is tied to the ground. About how high in the air is the hot air balloon?

A. 180 yds

B. 199 yds

C. 201 yds

D. 220 yds

30. Which set of measurements could be the side lengths of a right

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triangle?

A. {2 ft, 3 ft, 5 ft}

B. {3 ft, 6 ft, 9 ft}

C. {5 ft, 12 ft, 13 ft}

D. {6 ft, 9 ft, 12 ft}

31. What is the length of the hypotenuse, x, in the right triangle below?

A. 46 cm

B. 50 cm

C. 62 cm

32. Right triangle DEF has an area of 30 square centimeters (cm2). Segment DE has a length of 5 cm, and segment EF is the hypotenuse. What is the distance between point E and point F?

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A. 12 cm

B. 13 cm

C. 17 cm

D. 25 cm

33. Martha is in a hot air balloon that has risen straight up from the launch point. Matthew is standing on the ground, 16 meters away from the launch point. If Martha and Matthew are 20 meters apart, how high has the balloon risen?

A. 4 meters

B. 12 meters

C. 36 meters

D. 144 meters

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34. Triangle AOC intersects a circle with center O. Side AO is 10 inches (in.) and the diameter of the circle is 12 in., as shown below.

What is the length of

A. 10 inches

B. 14 inches

C. 15 inches

D. 16 inches


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What is the length of the hypotenuse of the triangle?

A. 41 cm

B. 31 cm

C. 25 cm

36. Mr. Lopez has a rectangular classroom that measures 36 feet by 28 feet. What is the approximate diagonal measurement of the room?

A. 23 feet

B. 44 feet

C. 46 feet

37. Which expression can be used to find the length of the third side of the triangle below?

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A.

B.

C.

D.

38. A section of bridge can be raised to allow tall ships to pass underneath.

Which distance, to the nearest tenth of a meter, is closest to the height that the bridge section is raised above its original horizontal position?

A. 10.2 m

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B. 20.4 m

C. 22.8 m

D. 36.8 m

39. One end of a pole is placed 5 feet (ft) from a wall, and the other end touches the wall 12 ft from the ground.

How long is the pole?

A. 7 ft

B. 13 ft

C. 15 ft

D. 17 ft

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40. What is the approximate length of in the right rectangular prism below?

A. 16.0 cm

B. 21.5 cm

C. 23.3 cm

D. 26.2 cm

41. Sarah left the boat dock and sailed 5 miles due east. She turned and then sailed 10 miles due north. About how far is Sarah from the boat dock?

A. 9 miles

B. 10 miles

C. 11 miles

D. 15 miles

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42. The front of a tent has the dimensions shown. The tent pole bisects the base.

What is the length of the side of the tent, x, in feet (ft)?

A.

B.

C.

D.

43. Heidi helped build a slide at the local park. The ladder is 4 feet high, and the slide is 5 feet long. How far is the bottom of the ladder from the bottom end of the slide?

A. 3 feet

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B. 4 feet

C. 5 feet

D. 6 feet

44. Figure PQRS below is made up of a rectangle and two right triangles.

What is the perimeter of figure PQRS?

A. 78 cm

B. 66 cm

C. 62 cm

D. 45 cm

45. A wire is attached to a pole and runs to the ground.

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About how high is the wire attached to the pole?

A. 3.7 m

B. 9.5 m

C. 12.5 m

D. 13.5 m

46. Dennis has a 15-foot ladder. He placed it 5 feet from the base of the house and then leaned the ladder against the house. About how far up the house does the ladder reach?

A. 20 feet

B. 18 feet

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C. 16 feet

D. 14 feet

47. Carolyn’s house is 15 miles south of Ben’s house. Paula’s house is 8 miles east of Carolyn’s house. What is the shortest distance between Ben’s house and Paula’s house?

A. 7 miles

B. 13 miles

C. 17 miles

D. 23 miles

48. A 40-foot wire is attached to a pole and runs to the ground as shown below. The pole is 35 feet tall.

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About how far away from the pole is the wire attached to the ground, x?

A. 19 feet

B. 53 feet

C. 75 feet

49. The length of a football field is 360 feet and the width is 160 feet. What is the approximate length of the diagonal of the football field?

A. 260 feet

B. 322 feet

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C. 394 feet

D. 416 feet

50. The length of the hypotenuse of a right triangle is 8 cm. The length of one of its legs is 6 cm. What is the approximate area of the right triangle?

A. 48 cm2

B. 32 cm2

C. 24 cm2

D. 16 cm2

51. A student used the triangle and equation shown to find x, the missing side length.

Which equation shows the correct result of the first step?

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A.

B.

C. 9 + 16 = x

D.

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