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Pythagorean Theorem and its Applications

Total questions: 36

Worksheet time: 4hrs 41mins

Name
Class
Date
1.

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

2.

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

3.

Marcus leans a 12-ft ladder against a wall to clean a window. If the base of the ladder is 3 ft away from the wall, how high up does the ladder reach? Round to the nearest tenth.

a)

12.4 feet

b)

10 feet

c)

11.6 feet

d)

10.6 feet

4.

A sailing ship sails 46 km North and then 74 km East. How far is the ship from its starting point to the nearest km?

a)

67 km

b)

58 km

c)

85 km

d)

87 km

5.

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

6.

A 12 foot ladder leans against the side of a house. The bottom of the latter is 8 ft from the side of the house. How high is the top if the ladder from the ground.

a)

The top of the ladder is 8.9 ft from the ground

b)

The top of the ladder is 9.2 ft from the ground

c)

The top of the ladder is 16.5 ft from the ground

d)

The top o the ladder is 14.4 ft from the ground

7.

Find the perimeter of a triangle that has legs that are 3 cm and 4 cm.

a)

5

b)

7

c)

10

d)

12

8.

Which set of numbers could represent a right triangle?

a)

a

b)

b

c)

c

d)

d

9.
a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?
a)
yes 
b)
no
10.
a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?
a)
yes 
b)
no
11.

Level 1

The Pythagorean Theorem works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

e)

all triangles

12.

Level 1

If a right triangle has side lengths 6, 7 and 3, which side is the hypotenuse?

a)

6

b)

7

c)

3

d)

49

e)

9

13.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

14.

Level 3

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

15.

Level 4

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

16.
What is the final step in solving this work for c?
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
a)
Divide both sides by 2
b)
Take the square root of both sides
17.

The Pythagorean Theorem is

a2 - b2 = c2

a)

false

b)

true

18.
Find the length of the missing side. 
a)
17 cm
b)
22 cm
c)
15 cm
d)
13 cm
19.
Would a triangle with these side lengths be a right triangle?
4, 5, 6
a)
Yes
b)
No
20.

Side c on a right triangle is ALWAYS the longest.

a)

true

b)

false

21.

Sides a and b are called legs.

a)

true

b)

false

22.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

23.
What if the value of x?
a)
16
b)
12
c)
4
d)
64
24.
Find the value of y. 
a)
4
b)
2√6
c)
6√2
d)
12
25.

Find the value of x.

a)

12

b)

4√2

c)

√32

d)

16

26.
x=?
a)
3
b)
5
c)
4
d)
6
27.

Find x.

a)

6

b)

10

c)

14

d)

8

28.

Solve for x.

a)

6

b)

8

c)

10

d)

12

29.

Solve for y.

a)

10.67

b)

6

c)

8

d)

12.33

30.

Solve for x.

a)

32

b)

24

c)

28

d)

30

31.
What is geometric mean of 4 and 9?
a)
5
b)
6
c)
7
d)
8
32.
Find the geometric mean for 4 and 9.
a)
6
b)
2√3
c)
3√2
d)
8
33.
Find the geometric mean for 2 and 25.
a)
5
b)
2√5
c)
2
d)
5√2
34.
Find the geometric mean for 6 and 8.
a)
16√3
b)
4√3
c)
3√4
d)
3√16
35.
Find the geometric mean for 5 and 25.
a)
5√5
b)
5
c)
5√2
d)
2√5
36.
Find the geometric mean for 3 and 9.
a)
3
b)
3√3
c)
9
d)
9√3

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