Free Printable Pythagorean Review

1.

Level 1

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

2.

Level 1

The Pythagorean Theorem is

a² + b²+ c²

a)

false

b)

true

3.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

4.

Level 3

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

5.

Level 3

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

6.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

3

7.

_{^{Find the missing side}}

a)

29.2

b)

20

c)

400

d)

10

8.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

9.

_{^{Find the missing side}}

a)

9

b)

26.9

c)

37

d)

18.2

10.

_{^{Find the missing side}}

a)

37

b)

17.66

c)

6

d)

312

11.

_{^{Find the missing side}}

a)

48

b)

108

c)

83.6

d)

72

12.

Determine the length of the missing side.

13.

Find h (hint: it is NOT 60 ft!)

14.

Find the value of x.

15.

solve for c

16.

Do the sides make a right triangle?

sides 9 ft, 20 ft, 14 ft

a)

no

b)

yes

17.

Do the sides make a right triangle?

sides 15 cm, 8 cm, 17 cm

a)

no

b)

yes

18.

Do the sides make a right triangle?

sides 12 in, 10 in, 8 in

a)

no

b)

yes

19.

Do the sides make a right triangle?

sides 20 m, 8m, 19 m

a)

no

b)

yes

20.

Which equation can be used to solve for "x"?

a)

15² – x² = 21²

b)

x² – 15² = 21²

c)

15² + 21² = x²

d)

21² – 15² = x²

21.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

22.

Sides a and b are called legs.

a)

true

b)

false

23.

Side a on a right triangle is ALWAYS the longest side.

a)

true

b)

false

24.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

25.

Find the distance between these two points.

a)

13

b)

7.9

c)

9.2

d)

3.6

26.

Which equation is modeled by the picture shown?

a)

3²+5²=4²

b)

3²+4²=5²

c)

5²+4²=3²

d)

9²+16²=25²

27.

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

28.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

29.

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

30.

Find the length of the missing side.

a)

48

b)

108

c)

83.6

d)

72

31.

Solve for x. SIMPLIFY your radical answer completely.

a)

√3

b)

3

c)

√41

d)

41

32.

Find the length of the missing side. (Calculators are allowed)

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

33.

Find the length of the missing side. (Calculators are allowed)

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

34.

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

35.

Would a triangle with these side lengths be a right triangle?
4, 5, 6

a)

Yes

b)

No

36.

What is the height of the cone?

a)

14 cm

b)

8 cm

c)

12 cm

d)

13.9 cm

37.

What is the length of the missing side? *NOTE: side lengths of 10 and 12.

a)

15.6

b)

6.6

c)

44

d)

16

38.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

39.

Level 4

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)

23 feet

b)

26 feet

c)

27 feet

d)

22 feet

40.

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

41.

Which equation can be used to solve for "x"?

a)

x² + 15² = 21²

b)

x² – 15² = 21²

c)

15² + 21² = x²

d)

x² + 21² = 15²

42.

What is

4^2

a)

4

b)

8

c)

16

d)

44

43.

What is

5^2+3^2

a)

9

b)

25

c)

16

d)

34

44.

What is side c called?

a)

Leg

b)

Hypotenuse

c)

$90\degree\$ angle

45.

What is side a and b called?

a)

Legs

b)

Hypotenuse

c)

$90\degree\$ angle

46.

Use the Pythagorean Theorem to solve for x.

a)

$\sqrt{1213}=34.8$

b)

$\sqrt{455}=21.3$

c)

$\sqrt{87}=9.3$

d)

$\sqrt{49}=7$

47.

What side of the right triangle is the x on?

a)

Leg

b)

Hypotenuse

c)

Right Angle

48.

Use the Pythagorean Theorem to solve for x.

a)

$\sqrt{1295.06}=35.98$

b)

$\sqrt{565.4}=23.8$

c)

$\sqrt{49.6}=7.04$

d)

$\sqrt{11.4}=3.38$

49.

Which equation is set up correctly for this word problem?

a)

$23^2+b^2=10^2$

b)

$10^2+b^2+23^2$

c)

$10^2+23^2=c^2$

d)

$a^2+23^2=c^2$

50.

a)

43

b)

$\sqrt{44.05}=6.6$

c)

$\sqrt{629}=25.1$

d)

$\sqrt{33}=5.74$

51.

Do these 3 side lengths form a right triangle?
13, 80, and 81?

a)

yes

b)

no

52.

If the sides of a triangle are 7, 24, and 25, is it a right triangle?

a)

yes

b)

no

53.

Isabella has sticks that are 10cm, 11cm, and 13cm long. Can she place the sticks together to form a right triangle? Justify your answer.

a)

No, because 10+11 does not equal 13

b)

No, because 100+121 does not equal 169

c)

Yes, because there is a small side, medium side and long side

d)

Yes, because a triangle has 3 sides

54.

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

55.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

a)

180 feet

b)

90 feet

c)

13.4 feet

d)

127.3 feet

56.

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

57.

Find the missing side length.

a)

$\sqrt[]{73}\ cm$

b)

$\sqrt[]{17}\ \ cm$

c)

$73\ \ cm$

d)

$\sqrt[]{13}\ \ cm$

58.

Find the missing side length.

a)

$\sqrt[]{5}\ ft$

b)

$\sqrt[]{493}\ ft$

c)

$\sqrt[]{31}\ ft$

d)

$\sqrt[]{155}\ ft$

59.

Find missing side

a)

$2\sqrt{5}$

b)

$\sqrt{20}$

c)

$2\sqrt{3}$

60.

Find the missing leg

a)

57.6

b)

66.1

c)

60

Pythagorean Review

Total questions: 60

Worksheet time: 4hrs 9mins

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