AnswersELPGEQ1 MJ Grade 8 Pre-Algebra - 1205070 HCPS V24Finding the Hypotenuse in Right Triangles

Finding the Hypotenuse in Right Triangles Answers

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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
2
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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
3

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
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

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

Question illustration
A
6 squared + 11 squared = c squared
Option A
B
6 squared + c squared = 11 squared
Option B
C
c squared minus 6 squared = 11 squared
Option C
D
11 squared minus 6 squared = c squared
Option D
6

How much longer is the hypotenuse of the triangle than its shorter leg?

Question illustration
A
2 ft
B
4 ft
C
8 ft
D
10 ft
7

Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot?

A
21.5 ft
B
25.0 ft
C
32.6 ft
D
37.7 ft
8

How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot.

A
14.5 ft
B
15.5 ft
C
17.0 ft
D
19.0 ft
9

Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?

Question illustration
A
0.68 miles
B
0.81 miles
C
1.15 miles
D
1.44 miles
10

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

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