wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Pythagorean Theorem & Distance Formula

Total questions: 50

Worksheet time: 4hrs 34mins

Name
Class
Date
1.

T/F The Pythagorean Theorem for right triangles where c is the longest side is

c2 = a2 - b2

a)

false

b)

true

c)

did you actually read the problem?

d)

subtraction?

e)

theoretical, so maybe not true

2.

What is the relationship between the sides in the Pythagorean Theorem shown?

a)

a + b = c

b)

a2 + b2 = c2

c)

a2 – b2 = c2

d)

a – b = c

3.

Which equation correctly reflects the right triangle shown?

a)

x2 + 142 = 202

b)

142 + 202 = x2

c)

142 – 202 = x2

d)

x2 – 142 = 202

4.

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

5.

Which Pythagorean Triple does the picture illustrate?

a)

4, 5, 6

b)

2, 3, 4

c)

3, 4, 5

d)

1, 2, 3

e)

9, 16, 25

6.

Which equation CANNOT be used to find the length of the missing side?

a)

122 + 132 = x2

b)

x2 + 122 = 132

c)

132 – 122 = x2

d)

132 – x2 = 122

7.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

e)

equilateral

8.

What is the opposite operation to squaring a number?

a)

divide

b)

multiply

c)

fractions

d)

square root

e)

cube

9.

What is the side of a right triangle opposite the right angle?

a)

square

b)

arm

c)

leg

d)

hypotenuse

e)

altitude

10.

What is the length of the hypotenuse in the triangle shown?

a)

3

b)

4

c)

5

d)

8

e)

7

11.

What is the value of "x"?

a)

28

b)

20

c)

10.6

d)

4

e)

272\sqrt{7}

12.

The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse?

a)

13

b)

14

c)

26

d)

34

13.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

e)

100 in.

14.

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)

12.7

15.

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

e)

not far enough, keep running

16.

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

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

e)

15 feet

17.

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

e)

23 miles

18.

What is the diagonal length of the 6 by 7 inch iPad?

a)

9.2 in

b)

11 in

c)

13 in

d)

9.6 in

e)

8 in

19.

What is NOT the distance between the two points?

a)

6.3

b)

 4×10\sqrt{4\times10}  

c)

6.7

d)

2102\sqrt{10}

e)

40\sqrt{40}

20.
Find the distance.
a)
9.7
b)
10.7
c)
11.7
d)
12.7
21.
Solve for x. SIMPLIFY your radical answer completely.
a)
4√2
b)
2√4
c)
2√2
d)
16√2
22.
Solve for x. SIMPLIFY your radical answer completely.
a)
4√22
b)
22√4
c)
22√2
d)
2√22
23.
Solve for x. SIMPLIFY your radical answer completely.
a)
119
b)
√119
c)
13
d)
√13
24.
Solve for x. SIMPLIFY your radical answer completely.
a)
2√6
b)
6√2
c)
4√6
d)
6√4
25.
Find the most simplified radical AND approximate answers for x.
a)
21√2 ≈ 29.7
b)
2√21 ≈ 9.2
c)
√116 ≈ 10.8
26.

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

27.
What is the length of the hypotenuse?
a)
33.5 cm
b)
45 cm
c)
6.7 cm
d)
15 cm
28.
What is the area of the third square?
a)
6.7 cm2
b)
33.5 cm2
c)
2025 cm2
d)
45 cm2
29.
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?
a)
12 in2
b)
144 in2
c)
194 in2
d)
13.9 in2
30.

Pythagoras was from Ancient _________

a)

Germany

b)

Italy

c)

Greece

d)

America

e)

Rome

31.

Pythagorean ____________ are a set of 3 integers that satisfy the Pythagorean Theorem.

a)

doubles

b)

squares

c)

triples

d)

Spirals

32.

Challenge!- Find the length of line segment WZ if the cube has side lengths of 10 inches

a)

10.4 in.

b)

14.1 in.

c)

17.3 in.

d)

10210\sqrt{2}

e)

16.4 in.

33.
What is the distance from point E to point B. YES, I said E to B!
(watch your units)
a)
3.6
b)
13 units 
c)
3.6 units 
d)
5 units 
34.
Find the length of the side WV.
a)
2.38 units 
b)
2.73 units
c)
√2 units
d)
2.83 units 
35.
Find the distance between (2, -75) and (10, 235).
a)
305.5
b)
308.6
c)
310.1
d)
315.3
36.

If a triangle can be made with the following sides, classify it as Acute, Right or Obtuse : 6cm, 8cm, 10cm

a)

Not a Triangle

b)

Acute

c)

Right

d)

Obtuse

37.

If a triangle can be made with the following sides, classify it as Acute, Right or Obtuse : 3cm, 5cm, 9cm

a)

Not a Triangle

b)

Acute

c)

Right

d)

Obtuse

38.

If a triangle can be made with the following sides, classify it as Acute, Right or Obtuse : 3cm, 5cm, 7cm

a)

Not a Triangle

b)

Acute

c)

Right

d)

Obtuse

39.
Find the distance between (-5, -8) and (-1, -16).
a)
8.9
b)
9.8
c)
10.3
d)
11
40.

Using the distance formula, find the distance from point (1,2) to point (5,4)

a)

4

b)

45

c)

4.5

d)

5.4

41.
What if the value of x?
a)
16
b)
12
c)
4
d)
64
42.
What is a possible third side to a triangle with side lengths of 13 and 4?
a)
9
b)
12
c)
8
d)
5
43.
Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6?
a)
6
b)
7
c)
5
d)
4
44.
Simplify:
a)
2√12
b)
4√12
c)
4√3
d)
16√3
45.
The area of a square is 117 square meters. Which best represents the length of a side of the square? 
a)
10.8 m
b)
11 m
c)
10 m
d)
11.2 m
46.

A perfect square is a number whose square root is ___________.

a)

Even

b)

irrational

c)

Whole Number

d)

Odd

47.
All the following are Perfect Squares except for which one?
a)
81
b)
121
c)
361
d)
198
48.
Between which two consecutive whole numbers is the√200? 
a)
13 and 14
b)
15 and 16
c)
14 and 15
d)
11 and 12
49.
x² = 121
What does x equal?
a)
11²
b)
11 and -11
c)
20 and 11
d)
12 and 1
50.

A circle has a center (0,0) and goes through point (6,8) What is the radius of the circle?

a)

6

b)

8

c)

10

d)

14

e)

100

Similar Resources on Wayground

Year 9 Exam Practice Quiz

53 questions

Year 9 Exam Practice Quiz

quiz

Worksheet

•

9th Grade

PREGUNTAS DE PREPARACION PAERA EXAMEN DE ELIPSE

45 questions

PREGUNTAS DE PREPARACION PAERA EXAMEN DE ELIPSE

quiz

Worksheet

•

11th Grade

Pemanasan Semester Genap

50 questions

Pemanasan Semester Genap

quiz

Worksheet

•

10th - 11th Grade

TES DIAGNOSTIK KELAS XII

50 questions

TES DIAGNOSTIK KELAS XII

quiz

Worksheet

•

12th Grade

Integrated Math Q3 Benchmark

50 questions

Integrated Math Q3 Benchmark

quiz

Worksheet

•

9th Grade

MATH 9 1st SUMMATIVE ASSESSMENT

50 questions

MATH 9 1st SUMMATIVE ASSESSMENT

quiz

Worksheet

•

9th Grade

OPERACIONES CON NÚMEROS ENTEROS

45 questions

OPERACIONES CON NÚMEROS ENTEROS

quiz

Worksheet

•

8th - 9th Grade

Evaluación 1 _ Matemáticas IV

50 questions

Evaluación 1 _ Matemáticas IV

quiz

Worksheet

•

10th Grade