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8-CHAPTER 8 TEST 2025-26

Total questions: 101

Worksheet time: 4hrs 5mins

Name
Class
Date
1.

Solving for the missing leg: If the length of one leg is 5 and the hypotenuse is 13, what is the length of the missing leg?

a)

7

b)

10

c)

15

d)

12

2.

Solving for the missing leg: Given that the length of one leg is 8 and the hypotenuse is 17, what is the length of the missing leg?

a)

10

b)

15

c)

20

d)

25

3.

Solving for the missing leg: If the length of one leg is 12 and the hypotenuse is 20, what is the length of the missing leg?

a)

16

b)

8

c)

10

d)

24

4.

Solving for the missing leg: Given that the length of one leg is 15 and the hypotenuse is 25, what is the length of the missing leg?

a)

18

b)

20

c)

10

d)

30

5.

Calculating the length of one leg: In a right-angled triangle, if the hypotenuse is 10 and the other leg is 6, what is the length of the missing leg?

a)

8

b)

5

c)

12

d)

4

6.

Calculating the length of one leg: If the hypotenuse is 26 and the other leg is 10, what is the length of the missing leg?

a)

16

b)

24

c)

30

d)

20

7.

Calculating the length of one leg: In a right-angled triangle, if the hypotenuse is 15 and the other leg is 9, what is the length of the missing leg?

a)

10

b)

6

c)

12

d)

18

8.

Finding the length of the other leg: In a right-angled triangle, if one leg is 7 and the hypotenuse is 25, what is the length of the other leg?

a)

18

b)

10

c)

30

d)

24

9.

Finding the length of the other leg: If one leg is 12 and the hypotenuse is 13, what is the length of the other leg?

a)

3

b)

10

c)

7

d)

5

10.

Finding the length of the other leg: In a right-angled triangle, if one leg is 20 and the hypotenuse is 29, what is the length of the other leg?

a)

25

b)

30

c)

10

d)

21

11.

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

a)

172+82=b217^2+8^2=b^2  

b)

82+b2=1728^2+b^2=17^2  

c)

172+b2=8217^2+b^2=8^2  

d)

82b2=172100\frac{8^2}{b^2}=\frac{17^2}{100}  

12.

How high is the ramp?

Round to the nearest tenth.

a)

28.3 ft.

b)

6.3 ft.

c)

8.9 ft.

d)

27.6 ft.

13.
Find the length of the missing side. 
a)
48 in.
b)
52 in.
c)
16 in.
d)
24 in.
14.

Find the length of the missing side

a)

48

b)

108

c)

83.6

d)

72

15.

Find the length of the missing side

a)

48

b)

108

c)

83.6

d)

72

16.
Find the length of the missing side. 
a)
48 in.
b)
52 in.
c)
16 in.
d)
24 in.
17.
Find the missing side
a)
29.2
b)
20
c)
400
d)
10
18.
Find the missing side
a)
36
b)
76.8
c)
12
d)
40
19.
Find the missing side
a)
9
b)
26.9
c)
37
d)
18.2
20.
Find the missing side
a)
37
b)
17.66
c)
6
d)
312
21.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

22.

Solving for the missing leg: If the length of one leg is 5 and the hypotenuse is 13, what is the length of the missing leg?

a)

7

b)

10

c)

15

d)

12

23.

Solving for the missing leg: Given that the length of one leg is 8 and the hypotenuse is 17, what is the length of the missing leg?

a)

10

b)

15

c)

20

d)

25

24.

Solving for the missing leg: If the length of one leg is 12 and the hypotenuse is 20, what is the length of the missing leg?

a)

16

b)

8

c)

10

d)

24

25.

Solving for the missing leg: Given that the length of one leg is 15 and the hypotenuse is 25, what is the length of the missing leg?

a)

18

b)

20

c)

10

d)

30

26.

Calculating the length of one leg: In a right-angled triangle, if the hypotenuse is 10 and the other leg is 6, what is the length of the missing leg?

a)

8

b)

5

c)

12

d)

4

27.

Calculating the length of one leg: If the hypotenuse is 26 and the other leg is 10, what is the length of the missing leg?

a)

16

b)

24

c)

30

d)

20

28.

Calculating the length of one leg: In a right-angled triangle, if the hypotenuse is 15 and the other leg is 9, what is the length of the missing leg?

a)

10

b)

6

c)

12

d)

18

29.

Finding the length of the other leg: In a right-angled triangle, if one leg is 7 and the hypotenuse is 25, what is the length of the other leg?

a)

18

b)

10

c)

30

d)

24

30.

Finding the length of the other leg: If one leg is 12 and the hypotenuse is 13, what is the length of the other leg?

a)

3

b)

10

c)

7

d)

5

31.

Finding the length of the other leg: In a right-angled triangle, if one leg is 20 and the hypotenuse is 29, what is the length of the other leg?

a)

25

b)

30

c)

10

d)

21

32.

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

a)

172+82=b217^2+8^2=b^2  

b)

82+b2=1728^2+b^2=17^2  

c)

172+b2=8217^2+b^2=8^2  

d)

82b2=172100\frac{8^2}{b^2}=\frac{17^2}{100}  

33.

How high is the ramp?

Round to the nearest tenth.

a)

28.3 ft.

b)

6.3 ft.

c)

8.9 ft.

d)

27.6 ft.

34.
Find the length of the missing side. 
a)
48 in.
b)
52 in.
c)
16 in.
d)
24 in.
35.

Find the length of the missing side

a)

48

b)

108

c)

83.6

d)

72

36.

Find the length of the missing side

a)

48

b)

108

c)

83.6

d)

72

37.
Find the length of the missing side. 
a)
48 in.
b)
52 in.
c)
16 in.
d)
24 in.
38.
Find the missing side
a)
29.2
b)
20
c)
400
d)
10
39.
Find the missing side
a)
36
b)
76.8
c)
12
d)
40
40.
Find the missing side
a)
9
b)
26.9
c)
37
d)
18.2
41.
Find the missing side
a)
37
b)
17.66
c)
6
d)
312
42.

Level 2

Solve for the value of y

a)

13

b)

5

c)

23

d)

10

43.
What is the opposite of squaring a number?
a)
divide
b)
multiply 
c)
fractions
d)
square root
44.

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

a)

5 cm

b)

7 cm

c)

10 cm

d)

12 cm

45.

What is the perimeter of a right triangle if the hypotenuse is 15 centimeters and one of the legs is 9 centimeters?

a)

36 cm

b)

39 cm

c)

41 cm

46.

Find the perimeter of the triangle.

a)

P=1,225 in

b)

P=1,369 in

c)

P=84 in

d)

P=35 in

47.
Find the perimeter of the triangle
a)
8
b)
22
c)
40
48.

”Real-world” word problems often have ladders leaning against trees, houses, or other structures. In these problems, the ladder represents the...

a)

Vertex

b)

Leg

c)

Right Angle

d)

Hypotenuse

49.

Jayson travels from his house directly west to the bank and then directly north from the bank to the mall. He then travels home on the road connecting the mall and his house. What is his total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

50.

CHALLENGE: Destiny leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches the skating rink for her birthday celebration.


How MUCH FURTHER did Destiny walk using this route instead of taking a straight shortcut path through Branch Brook Park to arrive at the skating rink? (Hint: Draw and label a model to help you visualize this situation.)

a)

4 blocks

b)

10 blocks

c)

14 blocks

d)

100 blocks

51.
Which of the following sentences would belong in the proof that describes this image?
a)
The sum of the areas of the two smaller squares is equal to the area of the large square.
b)
The sum of the side lengths of the two smaller squares is equal to the side length of the large square.
c)
The difference of the areas of the two smaller squares is equal to the area of the large square.
d)
The differences of the side lengths of the two smaller squares is equal to the side length of the large square.
52.

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

53.

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.9 feet

54.

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

55.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run?

a)

105 meters

b)

79.4 meters

c)

210 meters

d)

150 meters

56.

The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?

a)

375 in2

b)

70 in2

c)

300 in2

d)

20 in2

57.

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

58.

Two sides of a right triangle are 8 and 12. Find the missing side length if 8 and 12 are legs.

a)

4.5

b)

20

c)

8.9

d)

14.4

59.

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

60.

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

61.
Find the missing side
a)
9
b)
41
c)
6.4
d)
6.2
62.
Find the length of the missing side. 
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
63.
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
64.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
65.

Find the length of the missing side. 

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

66.

Find the length of the missing side. 

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

67.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
68.

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

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

69.

In a right triangle __________is ALWAYS the longest side.

a)

a leg

b)

a hypotenuse

70.

what is the formula for finding the hypotnuse?

a)

a2 + b2=c2

b)

a+b=c

c)

a2-b2=c2

d)

c2-a2=b

71.

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

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

72.

Find the missing side. (Calculators are allowed)

a)

48

b)

108

c)

83.6

d)

72

73.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
74.
a)
20 cm
b)
400 cm
c)
10 cm
d)
29.2 cm
75.
What is the length of x?
a)
5
b)
7
c)
8
d)
25
76.
a2 + b2 = c2
a = 9 b = 40
a)
c = 41
b)
c = 65
c)
c = 25
d)
c = 5
77.
If a triangle has a side a=5 and b=12, what is c?
a)
10
b)
17
c)
169
d)
13
78.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
79.
a2 + b2 = c2
b = 35 c = 37
a)
a = 12
b)
a = 11
c)
a = 18
d)
a = 14
80.
A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?
a)
111.8 yards
b)
115 yards
c)
127.3 yards
d)
119 yards
81.

What type of triangle will these side lengths form?

13, 12, 15

a)

Right

b)

Acute

c)

Obtuse

82.

What type of triangle will these side lengths form?

9, 12, 15

a)

Right

b)

Acute

c)

Obtuse

83.

What type of triangle will these side lengths form?

9, 10, 15

a)

Right

b)

Acute

c)

Obtuse

84.

What type of triangle will these side lengths form?

7, 8, 10

a)

Right

b)

Acute

c)

Obtuse

85.

What type of triangle will these side lengths form?

5, 12, 13

a)

Right

b)

Acute

c)

Obtuse

86.

What type of triangle will these side lengths form?

9, 11, 15

a)

Right

b)

Acute

c)

Obtuse

87.
State if the triangle is acute, obtuse, or right.
a)
acute
b)
obtuse
c)
right
88.
State if the triangle is acute, obtuse, or right.
a)
acute
b)
obtuse
c)
right
89.
State if the three sides lengths form an acute, obtuse, or right triangle:
4.8 km, 28.6 km. 29 km
a)
acute
b)
obtuse
c)
right
90.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
91.
State if the three sides lengths form an acute, obtuse, or right triangle:
6 mi, 17 mi, 2√55 mi
a)
acute
b)
obtuse
c)
right
92.
State if the three sides lengths form an acute, obtuse, or right triangle:
4.8 km, 28.6 km. 29 km
a)
acute
b)
obtuse
c)
right
93.

Determine what type (if any) of a triangle would have the following side lengths:


4, 6, 7

a)

acute

b)

obtuse

c)

right

d)

not a triangle

94.

Determine what type (if any) of a triangle would have the following side lengths:


21, 36, 39

a)

acute

b)

obtuse

c)

right

d)

not a triangle

95.

Determine what type (if any) of a triangle would have the following side lengths:


4, 6, 8

a)

acute

b)

obtuse

c)

right

d)

not a triangle

96.

Determine what type (if any) of a triangle would have the following side lengths:


10, 18, 40

a)

acute

b)

obtuse

c)

right

d)

not a triangle

97.

Determine what type (if any) of a triangle would have the following side lengths:


10, 18, 21

a)

acute

b)

obtuse

c)

right

d)

not a triangle

98.

Determine what type (if any) of a triangle would have the following side lengths:


13.5, 18, 22.5

a)

acute

b)

obtuse

c)

right

d)

not a triangle

99.

Determine what type (if any) of a triangle would have the following side lengths:


24, 52, 57

a)

acute

b)

obtuse

c)

right

d)

not a triangle

100.

Determine what type (if any) of a triangle would have the following side lengths:


24, 52, 60

a)

acute

b)

obtuse

c)

right

d)

not a triangle

101.

Determine what type (if any) of a triangle would have the following side lengths:


24, 52, 76

a)

acute

b)

obtuse

c)

right

d)

not a triangle

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