Free Printable Pythagorean Theorem Quiz Practice

1.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

2.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

3.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

4.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

5.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

6.

Use the Pythagorean Theorem to find the missing side length in the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

7.

A rectangular pool at Andy's gym measures 25 meters by 50 meters. How many meters would Andy need to swim in order to swim diagonally across the pool?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

8.

A pole vaulter rested a 17-foot pole against a wall. If the top of the pole hit the wall 14 feet above the ground, how far from the wall is the bottom of the pool?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi)

(a)

9.

What is the area of the largest square?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

10.

If the area of square 1 is 25 units², and the area of square 2 is 16 units², what is the perimeter of square 3?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

11.

Which equation would help you find the missing side length in the right triangle shown?

a)

$12^2-10^2=c^2$

b)

$12^2+b^2=10^2$

c)

$12\left(2\right)+10\left(2\right)=c\left(2\right)$

d)

$12^2+10^2=c^2$

12.

True or False?

The legs of a triangle are the sides adjacent to the right angle.

a)

True

b)

False

13.

True or False?

The hypotenuse is directly across from the right angle.

a)

True

b)

False

14.

True or False?

The Pythagorean Theorem can only be used with right triangles.

a)

True

b)

False

15.

True or False?

The hypotenuse is always the shortest side length.

a)

True

b)

False

16.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

17.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

18.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

19.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

20.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

21.

Find the missing side length of the the right triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

22.

If the area of square 1 is 250 units², and the area of square 3 is 120 units², what is the area of square 2?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

23.

Denise is using a ladder to clean the outside of her second story windows. The ladder she is using is 24 feet long, and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. How high up the side of her house does the ladder reach?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

24.

Will ran the diagonal distance across a square field measuring 40 yards on each side. James ran the diagonal distance across a rectangular field with a length of 25 yards and a width of 35 yards. How much farther did Will run?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

25.

Use the Pythagorean Theorem converse to prove whether or not the triangle is a right triangle.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

26.

Use the Pythagorean Theorem converse to prove whether or not the triangle is a right triangle.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

27.

Use the Pythagorean Theorem converse to prove whether or not the triangle is a right triangle.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

28.

Use the Pythagorean Theorem converse to prove whether or not the triangle is a right triangle.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

29.

Determine if the following side lengths would form a right triangle.

12, 24, and 36

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

30.

Determine if the following side lengths would form a right triangle.

16, 9 and 11

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

31.

Determine if the following side lengths would form a right triangle.

20, 29, and 21

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

32.

Determine if the following side lengths would form a right triangle.

12.5, 7.5, and 10

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

33.

Tyler thinks a window frame in his house looks slanted, because the corner doesn't appear to be a 90 degree angle. Cara thinks it looks fine. They measured the window to check and found the width to be 25 inches, the height to be 36 inches, and the diagonal distance to be 45 inches. Who is correct?

a)

Tyler

b)

Cara

34.

Patty wants a triangular garden in her backyard for all of her vegetables. She is going to use three pieces of fencing that measure 7 feet, 10 feet, and 8 feet. Will her garden be in the shape of a right triangle?

a)

Yes

b)

No

35.

The perimeters of three squares are shown. Could the three squares be positioned so that they meet to form a right triangle?

a)

Yes

b)

No

36.

Determine if the following side lengths would form a right triangle.

28, 53, and 45

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

37.

Determine if the following side lengths would form a right triangle.

4.5, 6, and 7.5

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

38.

Determine if the following side lengths would form a right triangle.

20, 40, and 30

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

39.

Determine if the following side lengths would form a right triangle.

50, 48, and 14

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

40.

Determine if the following side lengths would form a right triangle.

1, 2, and 5

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

41.

Determine if the following side lengths would form a right triangle.

25, 16, and 12

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

42.

Tina built a triangular sign with side lengths of 73 inches, 55 inches, and 48 inches. Is the sign a right triangle?

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

43.

Is the triangle shown a right triangle?

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

44.

Which of the following could be the areas of the three squares shown?

a)

12 ft², 16 ft², and 20 ft²

b)

10 ft², 18 ft², and 30 ft²

c)

4 ft², 5 ft², and 12 ft²

d)

8 ft², 16 ft², and 24 ft²

45.

Which of the following could be the perimeters of the three squares shown?

a)

12 ft, 16 ft, and 20 ft

b)

120 ft, 16 ft, and 24 ft

c)

40 ft, 80 ft, and 120 ft

d)

16 ft, 24 ft, and 28 ft

46.

Bethany's front door is a rectangle and has a width of 36 inches and a height of 80 inches. What is the diagonal distance of her door?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

47.

Greg plays baseball at a field where the baseball diamond is a square with each side of the square measuring 90 feet. If the baseball was thrown from home plate to 2nd base, how far did the baseball travel?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

48.

Melissa wants to put a ribbon border around a sign in her classroom shaped like a right triangle. If ribbon costs $0.82 per foot, how much will it cost her to buy the ribbon for her sign?

Don't forget to include a dollar sign in your answer and round to the nearest cent.

(a)

49.

In the isosceles triangle, the congruent sides each measure 13 meters. If the base of the triangle is 10 meters, what is the height of the triangle?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

50.

A square sandbox in Ty's backyard has an area of 81 square feet. Find x, the diagonal length of the sandbox.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

51.

To walk to her friends house, Julie normally walks 63 yards north and 16 yards east as shown. How many yards shorter would it be if Julie took the diagonal shortcut, x?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

52.

If the perimeter of square 3 is 36 units and the perimeter of square 2 is 48 units, what is the area of square 1?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

53.

Lincoln is building a wooden garage door in the shape of a rectangle with a width of 16 feet and a height of 8 feet. Lincoln is going to place two boards in the shape of an "X" on the door. How many feet of materials will he need for the "X"?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

54.

Lane rode his bike from Point A to B by using Cherry Street. How much further would his trip have been if he took Orange Drive and Peach Ave instead?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

55.

Ashton left his house and ran 4 miles east and then 3 miles north. he then took the diagonal path back home. If he burned 105 calories every mile that he ran, how many total calories did he burn on his run?

Use the unit "cal" after your answer.

(a)

56.

A family has a square field where they keep their cattle. The area of the field is 40,000 ft², and they want to put a fence diagonally through the field. What should the length of the fence be?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

57.

Caution tape needs to be placed diagonally across a rectangular door that is broken in a store. If the dimensions of the door are 3 feet by 7 feet, how many feet of caution tape will be needed?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

58.

In building a dog house, the front view of the roof is shown. What is the height of the roof?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

59.

If the area of square 2 is 225 units², and the perimeter of square 1 is 100 units, what is the area of square 3?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

60.

A farmer wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 8 feet, 15 feet, and 20 feet long.

Will he be able to make a right triangle with his fence?

a)

Yes

b)

No

61.

Find x, the missing side length in the right triangle.

Answer only with a number, no units required.

(a)

62.

Find x, the missing side length in the right triangle.

Answer only with a number, no units required.

(a)

63.

Find x, the missing side length in the right triangle.

Answer only with a number, no units required. Round to the nearest tenth, if necessary.

(a)

64.

Find x, the missing side length in the right triangle.

Answer only with a number, no units required. Round to the nearest tenth, if necessary.

(a)

65.

The legs of an isosceles right triangle both measure 10 inches. Find the length of the hypotenuse.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

66.

The longest side in a right triangle is 24 cm, and the second longest side is 20 cm. Find the length of the shortest side.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

67.

Peter is trying to get his cat out of a tree in his backyard. The cat is 12 feet above the ground, and Peter has to put the base of his ladder 9 feet away from the tree because of mud. How long does the ladder need to be in order to reach the cat?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

68.

The front view of a tent is shown. If a zipper is going to be put in along the length of x, how long should the zipper be?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

69.

Kevin is creating a target for a game that will be played at the school's carnival. In order to do this, Kevin needs to put red tape in the shape of an "x" as shown. If the area of the square board is 25 square feet, how many feet of tape will he need?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

70.

Gigi's family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn't stopped at the gas station and had driven along the diagonal path instead?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

71.

Use the Pythagorean Theorem to decide if this is a right triangle or not.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

72.

Use the Pythagorean Theorem to decide if this is a right triangle or not.

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

73.

Could the side lengths below form a right triangle?

61, 60, 11

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

74.

Could the side lengths below form a right triangle?

5, 7.5, 2.5

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

75.

The triangular sail on Ethan's sailboat measures 10.5 feet, 14 feet, and 17.5 feet on its three sides. Is the sail a right triangle?

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

76.

If the area of square 3 is 80 cm² and the area of square 2 is 100 cm², what is the area of square 1?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

77.

If the perimeter of square 1 is 104 feet and the area of square 2 is 576 ft², what is the side length of square 3?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

78.

Marvin is painting three squares shaped like the ones here. If it takes him exactly four cans of paint to paint square 3 and five cans of paint to paint 2, how many cans of paint should he need to paint square 1?

Answer with a number only, no units needed.

(a)

79.

Would the three squares here join together to make a right triangle?

a)

Yes, it is a right triangle.

b)

No, it is not a right triangle.

80.

True or False?

The hypotenuse is the longest side

a)

True

b)

False

81.

True or False?

The legs are the sides adjacent to the 90 degree angle.

a)

True

b)

False

82.

True or False?

The hypotenuse is always adjacent to the right angle.

a)

True

b)

False

83.

True or False?

Side "a" is always longer than side "b".

a)

True

b)

False

84.

True or False?

The hypotenuse is opposite the 90 degree angle.

a)

True

b)

False

85.

Joe needs to know if the triangle shown is a right triangle. Which equation could he use to help?

a)

$\sqrt{36}+\sqrt{25}=\sqrt{49}$

b)

$25+36=49$

c)

$25^2+36^2=49^2$

d)

$36^2-25^2=49^2$

86.

Find x, the missing side length in the right triangle.

Enter only a number. No unit needed.

(a)

87.

Which of the following could be the areas of the three squares shown?

a)

40 ft², 55 ft², 95 ft²

b)

35 ft², 25 ft², 45 ft²

c)

10 ft², 10 ft², 100 ft²

d)

40 ft², 30 ft², 1200 ft²

88.

Marcy's breakfast table has a square table top with an area of 36 square feet. What is the diagonal length of the table top?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

89.

The three squares shown join together to form a right triangle. The area and the perimeter for two of the squares is shown. Find the side length of the largest square.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

90.

Which of the following could not be the side lengths of a right triangle?

a)

7.5, 10, and 12.5

b)

85, 13, and 84

c)

37, 35, and 12

d)

24, 22, and 40

91.

Briana's backsplash in her kitchen is made up of square shaped tiles like the one shown here. The tiles are white with a black diagonal stripe. Which of the following would help her find x, the length of the black stripe?

a)

$4+4=x$

b)

$4^2+4^2=x$

c)

$4^2+4^2=x^2$

d)

$\sqrt{4}+\sqrt{4}=x$

92.

Find the perimeter of the isosceles triangle.

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

93.

Find x, the missing side length in the right triangle.

Enter only a number. No unit needed. Round to the nearest tenth if necessary.

(a)

94.

Quenten typically walks 28 yards south on Pine Street and 45 yards east on Maple Avenue in order to get to school. How much shorter would his walk be if he took the shortcut shown?

a)

73 yards

b)

20 yards

c)

53 yards

d)

126 yards

95.

Paul is building a bridge for a school project and wants to make a right triangle out of three popsicle sticks that measure 8 cm, 10 cm, and 18 cm. Can he make a right triangle out of these lengths?

a)

Yes, because $8+10=18$

b)

Yes, because $8^2+10^2=18^2$

c)

No, because $8\left(2\right)+10\left(2\right)\ne18\left(2\right)$

d)

No, because $8^2+10^2\ne18^2$

96.

In a football drill, Ron is standing 30 yards directly east of John, and Bill is standing 40 yards directly north of John. If the football is thrown from Ron to Bill and then from Bill to John, how many yards did the football travel?

Round to the nearest tenth, if necessary. Make sure to include the abbreviation for the correct unit in your answer. (Ex: 2 in or 8.5 mi) Place a 2 after a unit to represent units squared. (Ex: u2 or in2)

(a)

Pythagorean Theorem Quiz Practice

Total questions: 96

Worksheet time: 8hrs 0mins

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