AnswersPre-Algebra BUnit Test

Finding the Hypotenuse in Right Triangles Answers

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1
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Hans wanted to find the length of the hypotenuse of the triangle. Which statement correctly identifies his error?

Question illustration
A
He did not square 40, he just multiplied by 2.
B
He did not finish the problem. He should have divided 161 by 2 to find the square root.
C
He should have added 9 + 9 to find the value of .
Option C
D
He should have subtracted the two squares to get because numbers get too large if both legs are squared and then added together.
Option D
2
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What is the length of the hypotenuse of the triangle?

Question illustration
A
ft
Option A
B
ft
Option B
C
ft
Option C
D
ft
Option D
3

Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.

Question illustration
A
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
B
She did not square the 12 in the problem. She should have used .
Option B
C
She did not evaluate correctly. She should have used .
Option C
D
She did not evaluate correctly. She should have used .
Option D
E
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
F
She should not have added the squares in the first step. She should have used .
Option F
4

What is the length of the hypotenuse of the triangle?

Question illustration
A
26 ft
B
34 ft
C
68 ft
D
74 ft
5

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran miles, Colby ran 13 miles, and Arpitha ran the shortest route from the library to her house, as shown in the diagram. Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance?

Question illustration
A
Colby, Sanjay, Arpitha
B
Sanjay, Arpitha, Colby
C
Sanjay, Colby, Arpitha
D
Arpitha, Sanjay, Colby
6

Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he use to find the distance, d, that takes him directly back home?

Question illustration
A
2 squared + 3 squared = d squared
Option A
B
3 squared minus 2 squared = d squared
Option B
C
d squared + 2 squared = 3 squared
Option C
D
d squared + 3 squared = 2 squared
Option D
7

Mrs. Ibarra wants to create a right triangle for a geometry test. She plans to use 15, 36, and 41 as side lengths.Select the four true statements regarding the side lengths Mrs. Ibarra chose.

A
, so the side lengths will form a triangle.
Option A
B
, so those lengths will not form a triangle.
Option B
C
15 squared + 36 squared = 1,521
Option C
D
41 squared = 1,681
Option D
E
Since , it will not be a right triangle.
Option E
F
15 squared + 36 squared = 297
Option F
G
41 squared = 82
Option G
8

Which is the length of the hypotenuse of the triangle?

Question illustration
A
ft
Option A
B
ft
Option B
C
33 ft
D
37 ft
9

Which equation could be used to find the length of the hypotenuse?

Question illustration
A
5 squared + 8 squared = c squared
Option A
B
5 squared + c squared = 8 squared
Option B
C
c squared minus 5 squared = 8 squared
Option C
D
8 squared minus 5 squared = c squared
Option D
10

Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.What errors did Lewis make? Check all that apply.

Question illustration
A
He simplified incorrectly. It should be 20 instead of 200.
Option A
B
He found the difference between the hypotenuse and the short leg instead of the long leg.
C
He evaluated incorrectly. It should be .
Option C
D
He evaluated incorrectly. It should be .
Option D
E
He should not have taken the square root of each side to get rid of the exponent.

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