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#3-3 Applying Pythagorean Theorem

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

Brianna is planting a sapling. The garden center recommended she stabilize the sapling with guide wires for the first year.

a)

6.6 feet

b)

7.8 feet

c)

12.2 feet

d)

15.6 feet

2.
A 14-foot ladder is set up 4 feet from the base of a building.  How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
a)
13.4 feet
b)
14.6 feet
c)
16.5 feet
d)
18.0 feet
3.
What is the length of the diagonal of the rectangular solid shown?
a)
5 cm
b)
13 cm
c)
6cm
d)
12.3
4.

We are given one of the sides and the hypotenuse.

Find the length of the missing side length.

(Hint: distance from the wall to the bottom of the ladder)

a)

7

b)

5

c)

11

d)

25

5.
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
6.
Using the Pythagorean Theorem, find the area of the missing square (seen in picture)
a)
75 cm2
b)
105 cm2
c)
135 cm2
d)
30 cm2
7.

The slide at the playground has a height of 6 feet. The base (bottom) 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

8.

Find the area of the missing square off of leg A if the area of one square is 369 and the area of another is 81?

a)

21.2

b)

17

c)

450

d)

288

9.
If the area of square b is 144 ft2 and the length of side a is 5 ft, what is the area of square c?
a)
169 ft2
b)
13 ft2
c)
12.2 ft2
d)
10.9 ft2
10.

The diagram shows a rectangular field.

What is the length of the diagonal of the field?

a)

120 ft.

b)

200 ft.

c)

394 ft.

d)

520 ft.

11.
if a = 3 feet,  b = 8 feet,  and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?
a)
8.54 feet
b)
10.44 feet
c)
10 feet
d)
4.12 feet
12.

Which Pythagorean Triple does the picture illustrate?

a)

4, 5, 6

b)

2, 3, 4

c)

3, 4, 5

d)

1, 2, 3

13.
a)
7 ft
b)
5 ft
c)
3 ft
d)
2 ft
14.
What is the height of the cone? 
a)
14 cm
b)
8 cm
c)
12 cm
d)
13.9 cm
15.
if a = 3 feet,  b = 8 feet,  and c = 6 feet, what is the length of d rounded to the nearest hundredth of a foot?
a)
8.54 feet
b)
10.44 feet
c)
10 feet
d)
4.12 feet
16.
A 10-foot ladder is leaning against the wall.  The bottom of the ladder is 4 feet from the base of the wall.  Which of the following is closest to the distance from the top of the ladder to the base of the wall?
a)
9ft
b)
11ft
c)
6ft
d)
14ft
17.

Solve for x.

a)

38.9

b)

40.2

c)

45.6

d)

54

18.

Find the the length of diagonal AV in a three dimensional figure.

a)

10

b)

17

c)

13

d)

22

19.

The elementary school is building a new jungle gym for their playground. The builders designed it so that it is the shape of a large rectangular prism with one diagonal on the front side of the structure. The sides measures 4 meters by 3 meters by 2 meters. What is the length of the diagonal that will brace the jungle gym ?

a)

13 meters

b)

20 meters

c)

25 meters

d)

5 meters

20.

John wants to fence off a triangle 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