Free Printable Unit 18 Retake (P.T. & G.M.)

1.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

2.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

3.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

4.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

5.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

6.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

7.

Determine if the following set of numbers are Pythagorean Triples.
15, 20, 25

a)

Yes

b)

No

8.

Determine if the following set of numbers are Pythagorean Triples.
18, 73, 75

a)

Yes

b)

No

9.

If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third number?

a)

45

b)

50

c)

55

d)

60

10.

Does the set of numbers represent a Pythagorean Triple.
15, 20, 25

a)

Yes

b)

No

11.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

12.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

13.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

14.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

15.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

16.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

17.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

18.

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

a)

7.5 in

b)

12.4 in

c)

13.6 in

d)

14.3 in

19.

To get from one side of the pond to the other you must walk 34 meters south and 41 meters east. To the nearest meter, how many less meters would it take if it were possible to go directly across the pond.

a)

53

b)

22

c)

75

d)

9

20.

Johnathan is painting the side of his home. He has a 25 foot ladder and leans the ladder against his house. The base of the ladder is five feet from the side of the house. How far up the house will the ladder reach?

a)

24.5 ft

b)

25.5 ft

c)

26.5 ft

d)

23.5 ft

21.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Which diagram best represents the problem?

a)

b)

c)

d)

22.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Which equation could be used to solve the problem?

a)

$25^2+10^2=c^2$

b)

$25^2+b^2=10^2$

c)

$a^2+10^2=25^2$

d)

$10^2+b^2=25^2$

23.

Larry attached a string from the top of the flagpole to the ground. The flagpole is 26 feet high and the string is 18 feet away from the flagpole. How long is the string?

a)

352 feet

b)

31.6 feet

c)

44 feet

d)

6.6 feet

24.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

25.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

26.

Madison is on the top of an 80 foot building. She is creating a zipline course to the ground with 100 feet of cable. How far from the base of the building will she need to anchor the cable to make the zipline cable tight?

a)

60 feet

b)

20 feet

c)

180 feet

27.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

28.

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

a)

6

b)

6.7

c)

3

d)

15.7

e)

None of them

29.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

30.

Trista's TV screen is 17 inches long. If the diagonal measures 22 inches, how long is the width of Donna's TV?

a)

5 in

b)

10 in

c)

14 in

d)

28 in

31.

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance back to their starting point to the nearest tenth of a mile?

a)

13

b)

9.4

c)

6.2

d)

9

32.

Level 3

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

33.

Determine if the following set of numbers are Pythagorean Triples.
15, 20, 25

a)

Yes

b)

No

34.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

35.

Determine if the following set of numbers are Pythagorean Triples.
18, 73, 75

a)

Yes

b)

No

36.

Find the value of x.

a)

75

b)

68.9

c)

76

d)

70

37.

a² + b² = c^{2
b = 35 c = 37}

a)

a = 12

b)

a = 11

c)

a = 18

d)

a = 14

38.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Which diagram best represents the problem?

a)

b)

c)

d)

39.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

40.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Which equation could be used to solve the problem?

a)

$25^2+10^2=c^2$

b)

$25^2+b^2=10^2$

c)

$a^2+10^2=25^2$

d)

$10^2+b^2=25^2$

41.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

42.

Larry attached a string from the top of the flagpole to the ground. The flagpole is 26 feet high and the string is 18 feet away from the flagpole. How long is the string?

a)

352 feet

b)

31.6 feet

c)

44 feet

d)

6.6 feet

43.

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

a)

111.8 yards

b)

115 yards

c)

127.3 yards

d)

119 yards

44.

Madison is on the top of an 80 foot building. She is creating a zipline course to the ground with 100 feet of cable. How far from the base of the building will she need to anchor the cable to make the zipline cable tight?

a)

60 feet

b)

20 feet

c)

180 feet

45.

Two joggers run 8 miles north and then 5 miles west. What is the shortest distance back to their starting point to the nearest tenth of a mile?

a)

13

b)

9.4

c)

6.2

d)

9

46.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

47.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.9 feet

48.

In the Old West, settlers made tents out of a piece of cloth thrown over a clothesline and then secured it to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide?

a)

14.4 feet

b)

7.2 feet

c)

10 feet

d)

20 feet

49.

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

50.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run?

a)

105 meters

b)

79.4 meters

c)

210 meters

d)

150 meters

51.

The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?

a)

375 in²

b)

70 in²

c)

300 in²

d)

20 in²

52.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

53.

Two sides of a right triangle are 8 and 12. Find the missing side length if 8 and 12 are legs.

a)

4.5

b)

20

c)

8.9

d)

14.4

54.

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

a)

9 feet

b)

19.2 feet

c)

81 feet

d)

369 feet

55.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

56.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

6.2

57.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

58.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

59.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

60.

Find the length of AB.

a)

36

b)

18

c)

6

d)

12

61.

The accompanying diagram shows a 24-foot ladder leaning against a building. A steel brace extends from the ladder to the point where the building meets the ground. The brace forms a right angle with the ladder.If the steel brace is connected to the ladder at a point that is 10 feet from the foot of the ladder, which equation can be used to find the length, x, of the steel brace?

a)

$\frac{10}{x}=\frac{x}{14}$

b)

$\frac{10}{x}=\frac{x}{24}$

c)

$10^2+x^2=14^2$

d)

$10^2+x^2=24^2$

62.

In right triangle ABC below, CD is the altitude to hypotenuse AB. If CD=6 and the ratio of AD to AB is 1:5, determine and state the length of BD.

a)

2.68

b)

7.2

c)

14.4

d)

3.1

63.

How far is it across the lake?

a)

4

b)

6

c)

9

d)

12

64.

In the accompanying diagram, triangle ABC is a right triangle and CD is the altitude to hypotenuse AB. If AD=4 and DB=16 find the length of CD.

a)

0

b)

64

c)

8

d)

32

65.

In the accompanying diagram of right triangle ABC, CD is drawn perpendicular to hypotenuse AB. If AB=16 and DB=4 find the length of BC.

a)

0

b)

8

c)

32

d)

64

66.

In right triangle ABC, altitude CD is drawn to hypotenuse AB. Find the length of BC.

a)

80

b)

40

c)

0

d)

8.9

67.

Find the length of the altitude of triangle PQR.

a)

6.9

b)

48

c)

24

d)

0

68.

Find the length HK of of right triangle GHK.

a)

300

b)

0

c)

150

d)

17.3

69.

Find the value of x.

a)

0

b)

48

c)

4.9

d)

24

70.

If AD=3, AB=8, find the value of CB.

a)

6.3

b)

40

c)

80

d)

20

71.

Find the value of x.

a)

12

b)

16

c)

9

d)

6

72.

Find the value of y, if you know the value of x=16

a)

400

b)

20

c)

200

d)

40

73.

Find the value of z, if you know the value of x=16.

a)

30

b)

112.5

c)

225

d)

15

74.

In the right triangle ABC below, CD is the altitude to the hypotenuse AB. If AC=28, and the ratio of AD to AB is 4:3, determine the value of x.

a)

28

b)

$4\sqrt{7}$

c)

$7\sqrt{2}$

d)

$2\sqrt{7}$

75.

In the right triangle ABC below, CD is the altitude to the hypotenuse AB. If AD=3, AB=12, what is the value of CB?

a)

120

b)

$4\sqrt{15}$

c)

$2\sqrt{30}$

d)

$2\sqrt{10}$

76.

What is the formula for Geometric Mean?

a)

$\frac{height}{leg}=\frac{leg}{height}$

b)

$\frac{leg}{height}=\frac{leg}{height}$

77.

What if the value of x?

a)

16

b)

12

c)

4

d)

64

78.

Find the value of y.

a)

4

b)

2√6

c)

6√2

d)

12

79.

Find the value of x.

a)

12

b)

4√2

c)

√32

d)

16

80.

x=?

a)

3

b)

5

c)

4

d)

6

81.

Find x.

a)

6

b)

10

c)

14

d)

8

82.

Solve for x.

a)

6

b)

8

c)

10

d)

12

83.

Solve for y.

a)

10.67

b)

6

c)

8

d)

12.33

84.

Solve for x.

a)

32

b)

24

c)

28

d)

30

85.

Evelina is hanging silver stars from the gym ceiling using string for the homecoming dance. Find the height from the floor (F) to the ceiling (C).

a)

20 ft

b)

25 ft

c)

42 ft

d)

15 ft

86.

Find the approximate height of the waterfall.

a)

156.8 ft

b)

161.8 ft

c)

33 ft

d)

140 ft

87.

How tall is the cliff?

a)

588 ft

b)

591 ft

c)

600 ft

d)

569 ft

Unit 18 Retake (P.T. & G.M.)

Total questions: 87

Worksheet time: 6hrs 2mins

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