Free Printable Pythagorean Theorem Word Problems

Worksheets

Pythagorean Theorem Word Problems

Total questions: 50

Worksheet time: 13hrs 30mins

Name

Class

Date

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?

25 feet

26 feet

27 feet

28 feet

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?

5.3

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?

7.5 in

12.4 in

13.6 in

14.3 in

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.

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?

24.5 ft

25.5 ft

26.5 ft

23.5 ft

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?

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?

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

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

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

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

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?

352 feet

31.6 feet

44 feet

6.6 feet

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

111.8 yards

115 yards

127.3 yards

119 yards

10.

The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

11.

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?

60 feet

20 feet

180 feet

12.

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

44.1 km

59 km

47.8 km

33 km

13.

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

6.7

15.7

None of them

14.

Level 2

Solve for the value of y

15.

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

5 in

10 in

14 in

28 in

16.

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?

9.4

6.2

17.

Level 3

Find the length of the missing side.

25 cm

42 cm

52 cm

48 cm

18.

The Pythagorean Theorem ONLY works on which triangle?

obtuse

scalene

isosceles

right

19.

The two shortest sides of a right triangle are called___________.

arms.

hypotenuses.

legs.

rays.

20.

The longest side of a right triangle.

Leg 1

Leg 2

Perimeter

Hypotenuse

21.

Durham and Chapel Hill are 14 miles apart. Chapel Hill and Raleigh are 28 miles part. Raleigh and Durham are 25 miles part. Do these three cities form a right triangle?

Yes they form a right triangle

No they do not form a right triangle

22.

Which set of sides would make a right triangle?

4,5,6

8,10,12

5,12,13

5,10,12

23.

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?

Round your answer to the tenths place if needed.

9 feet

19.2 feet

81 feet

369 feet

24.

Your family just bought you a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), How wide is the laptop screen if the height was 10 inches?

Round your answer to the tenths place if needed.

7 inches

10 inches

19.7 inches

13.7 inches

25.

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)

Round your answer to the tenths place if needed.

180 feet

90 feet

13.4 feet

127.3 feet

26.

If a 25-foot ladder leans against a building and the foot of the ladder is 7 feet from the base of the building, how far up the building does the ladder reach?

576 ft

24 ft

4.2 ft

18 ft

27.

A 40-foot pole has a wire from the top to a point 9 feet from the base. How long is the wire?

1519 ft

31 ft

1681 ft

41 ft

28.

Find side "h" (wall height)

35.60

35.00

35.71

61.03

29.

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?

8 feet

5.29 feet

10 feet

14 feet

30.

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

6.7

15.7

None of them

31.

Level 2

Solve for the value of y

32.

^{Find the missing side}

$\sqrt{61}$

$\sqrt{11}$

33.

A flat screen TV in the shape of a rectangle has a width of 36 inches and a height of 20 inches. Find the length of the diagonal.

(a)

34.

A 20-foot piece of wire is attached from the top of a flagpole to a stake in the ground 8 feet from the base of the pole. Find the height of the flagpole.

(a)

35.

A 14-foot ladder is leaned against a wall. If the base of the ladder is 6 feet from the wall, how high up the wall will the ladder reach?

(a)

36.

Joel and Levi spotted a bear in the woods while riding their bikes. Joel took off 3 miles north and Levi rapidly pedaled 2 miles east away from the bear. How far apart are the two boys?

(a)

37.

How far from the base of a house should you place an 18-foot ladder if it must reach a window that is 15 feet high?

(a)

38.

An isosceles triangle has congruent legs that measure 10 feet. If the height of the triangle is 7 feet, find the length of its base.

(a)

39.

A football field is 120 yards long by 53 yards wide. If a player runs diagonally from one corner to the opposite corner, how far will they travel?

(a)

40.

On a map, Norristown is 18 miles south of Lincoln, and Lincoln is 29 miles west of Allenport. Find the distance from Norristown to Allenport.

(a)

41.

A set of stairs is 10 feet high and covers a horizontal distance of 12 feet. If a handrail is to be installed that extends from the bottom to the top of the stairs, what length must it be?

(a)

42.

Jaycee is flying a kite at the park using a string that is 42 meters long. She notices that the kite is directly above her friend Maddy. If Jaycee and Maddy are standing 36 meters apart, How high is the kite?

(a)

43.

^{Find the closest length of the missing side.}

640

6.40

44.

Find the length of the missing side.

48 in.

52 in.

16 in.

24 in.

45.

What is the area of the third square?

6.7 cm²

33.5 cm²

2025 cm²

45 cm²

46.

What is the length of the hypotenuse?

33.5 cm

45 cm

6.7 cm

15 cm

47.

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

12 in²

144 in²

194 in²

13.9 in²

48.

Which equation is modeled by the picture shown?

3²+5²=4²

3²+4²=5²

5²+4²=3²

9²+16²=25²

49.

Do the segment lengths 15, 12, and 9 form a right triangle?

Yes

Maybe

Pythagoras

50.

Does the set of numbers represent a right triangle?

20, 25, 15

Yes

100 %

Pythagorean Theorem Word Problems

Total questions: 50

Worksheet time: 13hrs 30mins

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